[{"publication_identifier":{"issn":["1364-503X","1471-2962"]},"citation":{"mla":"Kaloshin, Vadim, and Alfonso Sorrentino. “On the Integrability of Birkhoff Billiards.” <i>Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences</i>, vol. 376, no. 2131, 20170419, The Royal Society, 2018, doi:<a href=\"https://doi.org/10.1098/rsta.2017.0419\">10.1098/rsta.2017.0419</a>.","apa":"Kaloshin, V., &#38; Sorrentino, A. (2018). On the integrability of Birkhoff billiards. <i>Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences</i>. The Royal Society. <a href=\"https://doi.org/10.1098/rsta.2017.0419\">https://doi.org/10.1098/rsta.2017.0419</a>","ieee":"V. Kaloshin and A. Sorrentino, “On the integrability of Birkhoff billiards,” <i>Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences</i>, vol. 376, no. 2131. The Royal Society, 2018.","ama":"Kaloshin V, Sorrentino A. On the integrability of Birkhoff billiards. <i>Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences</i>. 2018;376(2131). doi:<a href=\"https://doi.org/10.1098/rsta.2017.0419\">10.1098/rsta.2017.0419</a>","chicago":"Kaloshin, Vadim, and Alfonso Sorrentino. “On the Integrability of Birkhoff Billiards.” <i>Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences</i>. The Royal Society, 2018. <a href=\"https://doi.org/10.1098/rsta.2017.0419\">https://doi.org/10.1098/rsta.2017.0419</a>.","ista":"Kaloshin V, Sorrentino A. 2018. On the integrability of Birkhoff billiards. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. 376(2131), 20170419.","short":"V. Kaloshin, A. Sorrentino, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376 (2018)."},"fulldoi":"https://doi.org/10.1098/rsta.2017.0419","article_type":"original","day":"28","month":"10","oa_version":"None","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_created":"2020-09-17T10:42:01Z","date_updated":"2021-01-12T08:19:09Z","doi":"10.1098/rsta.2017.0419","type":"journal_article","issue":"2131","article_number":"20170419","keyword":["General Engineering","General Physics and Astronomy","General Mathematics"],"quality_controlled":"1","_id":"8419","publisher":"The Royal Society","article_processing_charge":"No","volume":376,"publication":"Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences","abstract":[{"lang":"eng","text":"In this survey, we provide a concise introduction to convex billiards and describe some recent results, obtained by the authors and collaborators, on the classification of integrable billiards, namely the so-called Birkhoff conjecture.\r\n\r\nThis article is part of the theme issue ‘Finite dimensional integrable systems: new trends and methods’."}],"language":[{"iso":"eng"}],"intvolume":"       376","status":"public","publication_status":"published","extern":"1","year":"2018","title":"On the integrability of Birkhoff billiards","author":[{"last_name":"Kaloshin","orcid":"0000-0002-6051-2628","first_name":"Vadim","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","full_name":"Kaloshin, Vadim"},{"last_name":"Sorrentino","first_name":"Alfonso","full_name":"Sorrentino, Alfonso"}],"date_published":"2018-10-28T00:00:00Z"},{"day":"15","article_type":"original","oa":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1706.07968"}],"publication_identifier":{"issn":["0951-7715","1361-6544"]},"fulldoi":"https://doi.org/10.1088/1361-6544/aadc12","citation":{"short":"V. Kaloshin, K. Zhang, Nonlinearity 31 (2018) 5214–5234.","ista":"Kaloshin V, Zhang K. 2018. Density of convex billiards with rational caustics. Nonlinearity. 31(11), 5214–5234.","chicago":"Kaloshin, Vadim, and Ke Zhang. “Density of Convex Billiards with Rational Caustics.” <i>Nonlinearity</i>. IOP Publishing, 2018. <a href=\"https://doi.org/10.1088/1361-6544/aadc12\">https://doi.org/10.1088/1361-6544/aadc12</a>.","ama":"Kaloshin V, Zhang K. Density of convex billiards with rational caustics. <i>Nonlinearity</i>. 2018;31(11):5214-5234. doi:<a href=\"https://doi.org/10.1088/1361-6544/aadc12\">10.1088/1361-6544/aadc12</a>","apa":"Kaloshin, V., &#38; Zhang, K. (2018). Density of convex billiards with rational caustics. <i>Nonlinearity</i>. IOP Publishing. <a href=\"https://doi.org/10.1088/1361-6544/aadc12\">https://doi.org/10.1088/1361-6544/aadc12</a>","ieee":"V. Kaloshin and K. Zhang, “Density of convex billiards with rational caustics,” <i>Nonlinearity</i>, vol. 31, no. 11. IOP Publishing, pp. 5214–5234, 2018.","mla":"Kaloshin, Vadim, and Ke Zhang. “Density of Convex Billiards with Rational Caustics.” <i>Nonlinearity</i>, vol. 31, no. 11, IOP Publishing, 2018, pp. 5214–34, doi:<a href=\"https://doi.org/10.1088/1361-6544/aadc12\">10.1088/1361-6544/aadc12</a>."},"page":"5214-5234","type":"journal_article","date_updated":"2021-01-12T08:19:10Z","date_created":"2020-09-17T10:42:09Z","doi":"10.1088/1361-6544/aadc12","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","arxiv":1,"oa_version":"Preprint","month":"10","status":"public","language":[{"iso":"eng"}],"intvolume":"        31","abstract":[{"lang":"eng","text":"We show that in the space of all convex billiard boundaries, the set of boundaries with rational caustics is dense. More precisely, the set of billiard boundaries with caustics of rotation number 1/q is polynomially sense in the smooth case, and exponentially dense in the analytic case."}],"publication":"Nonlinearity","volume":31,"article_processing_charge":"No","publisher":"IOP Publishing","_id":"8420","quality_controlled":"1","keyword":["Mathematical Physics","General Physics and Astronomy","Applied Mathematics","Statistical and Nonlinear Physics"],"external_id":{"arxiv":["1706.07968"]},"issue":"11","date_published":"2018-10-15T00:00:00Z","title":"Density of convex billiards with rational caustics","author":[{"full_name":"Kaloshin, Vadim","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","first_name":"Vadim","orcid":"0000-0002-6051-2628","last_name":"Kaloshin"},{"full_name":"Zhang, Ke","last_name":"Zhang","first_name":"Ke"}],"year":"2018","publication_status":"published","extern":"1"},{"article_type":"original","day":"02","citation":{"ama":"Dütting P, Henzinger M, Weber I. An expressive mechanism for auctions on the web. <i>ACM Transactions on Economics and Computation</i>. 2015;4(1). doi:<a href=\"https://doi.org/10.1145/2716312\">10.1145/2716312</a>","ieee":"P. Dütting, M. Henzinger, and I. Weber, “An expressive mechanism for auctions on the web,” <i>ACM Transactions on Economics and Computation</i>, vol. 4, no. 1. Association for Computing Machinery, 2015.","mla":"Dütting, Paul, et al. “An Expressive Mechanism for Auctions on the Web.” <i>ACM Transactions on Economics and Computation</i>, vol. 4, no. 1, 1, Association for Computing Machinery, 2015, doi:<a href=\"https://doi.org/10.1145/2716312\">10.1145/2716312</a>.","apa":"Dütting, P., Henzinger, M., &#38; Weber, I. (2015). An expressive mechanism for auctions on the web. <i>ACM Transactions on Economics and Computation</i>. Association for Computing Machinery. <a href=\"https://doi.org/10.1145/2716312\">https://doi.org/10.1145/2716312</a>","ista":"Dütting P, Henzinger M, Weber I. 2015. An expressive mechanism for auctions on the web. ACM Transactions on Economics and Computation. 4(1), 1.","chicago":"Dütting, Paul, Monika Henzinger, and Ingmar Weber. “An Expressive Mechanism for Auctions on the Web.” <i>ACM Transactions on Economics and Computation</i>. Association for Computing Machinery, 2015. <a href=\"https://doi.org/10.1145/2716312\">https://doi.org/10.1145/2716312</a>.","short":"P. Dütting, M. Henzinger, I. Weber, ACM Transactions on Economics and Computation 4 (2015)."},"fulldoi":"https://doi.org/10.1145/2716312","publication_identifier":{"issn":["2167-8375"],"eissn":["2167-8383"]},"scopus_import":"1","type":"journal_article","month":"12","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"None","doi":"10.1145/2716312","date_created":"2022-07-27T12:43:18Z","date_updated":"2024-11-06T12:07:05Z","publication":"ACM Transactions on Economics and Computation","volume":4,"status":"public","acknowledgement":"We would like to thank Veronika Loitzenbauer and the anonymous referees for their valuable feedback.","intvolume":"         4","language":[{"iso":"eng"}],"abstract":[{"lang":"eng","text":"Auctions are widely used on the Web. Applications range from sponsored search to platforms such as eBay. In these and in many other applications the auctions in use are single-/multi-item auctions with unit demand. The main drawback of standard mechanisms for this type of auctions, such as VCG and GSP, is the limited expressiveness that they offer to the bidders. The General Auction Mechanism (GAM) of Aggarwal et al. [2009] takes a first step toward addressing the problem of limited expressiveness by computing a bidder optimal, envy-free outcome for linear utility functions with identical slopes and a single discontinuity per bidder-item pair. We show that in many practical situations this does not suffice to adequately model the preferences of the bidders, and we overcome this problem by presenting the first mechanism for piecewise linear utility functions with nonidentical slopes and multiple discontinuities. Our mechanism runs in polynomial time. Like GAM it is incentive compatible for inputs that fulfill a certain nondegeneracy assumption, but our requirement is more general than the requirement of GAM. For discontinuous utility functions that are nondegenerate as well as for continuous utility functions the outcome of our mechanism is a competitive equilibrium. We also show how our mechanism can be used to compute approximately bidder optimal, envy-free outcomes for a general class of continuous utility functions via piecewise linear approximation. Finally, we prove hardness results for even more expressive settings."}],"issue":"1","article_number":"1","keyword":["Computational Mathematics","Marketing","Economics and Econometrics","Statistics and Probability","Computer Science (miscellaneous)"],"quality_controlled":"1","_id":"11670","publisher":"Association for Computing Machinery","article_processing_charge":"No","author":[{"full_name":"Dütting, Paul","first_name":"Paul","last_name":"Dütting"},{"last_name":"Henzinger","first_name":"Monika H","orcid":"0000-0002-5008-6530","id":"540c9bbd-f2de-11ec-812d-d04a5be85630","full_name":"Henzinger, Monika H"},{"full_name":"Weber, Ingmar","first_name":"Ingmar","last_name":"Weber"}],"title":"An expressive mechanism for auctions on the web","date_published":"2015-12-02T00:00:00Z","publication_status":"published","extern":"1","year":"2015"},{"day":"30","article_type":"original","fulldoi":"https://doi.org/10.1088/0951-7715/28/8/2699","citation":{"short":"V. Kaloshin, K. Zhang, Nonlinearity 28 (2015) 2699–2720.","chicago":"Kaloshin, Vadim, and K Zhang. “Arnold Diffusion for Smooth Convex Systems of Two and a Half Degrees of Freedom.” <i>Nonlinearity</i>. IOP Publishing, 2015. <a href=\"https://doi.org/10.1088/0951-7715/28/8/2699\">https://doi.org/10.1088/0951-7715/28/8/2699</a>.","ista":"Kaloshin V, Zhang K. 2015. Arnold diffusion for smooth convex systems of two and a half degrees of freedom. Nonlinearity. 28(8), 2699–2720.","ieee":"V. Kaloshin and K. Zhang, “Arnold diffusion for smooth convex systems of two and a half degrees of freedom,” <i>Nonlinearity</i>, vol. 28, no. 8. IOP Publishing, pp. 2699–2720, 2015.","apa":"Kaloshin, V., &#38; Zhang, K. (2015). Arnold diffusion for smooth convex systems of two and a half degrees of freedom. <i>Nonlinearity</i>. IOP Publishing. <a href=\"https://doi.org/10.1088/0951-7715/28/8/2699\">https://doi.org/10.1088/0951-7715/28/8/2699</a>","mla":"Kaloshin, Vadim, and K. Zhang. “Arnold Diffusion for Smooth Convex Systems of Two and a Half Degrees of Freedom.” <i>Nonlinearity</i>, vol. 28, no. 8, IOP Publishing, 2015, pp. 2699–720, doi:<a href=\"https://doi.org/10.1088/0951-7715/28/8/2699\">10.1088/0951-7715/28/8/2699</a>.","ama":"Kaloshin V, Zhang K. Arnold diffusion for smooth convex systems of two and a half degrees of freedom. <i>Nonlinearity</i>. 2015;28(8):2699-2720. doi:<a href=\"https://doi.org/10.1088/0951-7715/28/8/2699\">10.1088/0951-7715/28/8/2699</a>"},"publication_identifier":{"issn":["0951-7715","1361-6544"]},"page":"2699-2720","type":"journal_article","date_created":"2020-09-18T10:46:43Z","doi":"10.1088/0951-7715/28/8/2699","date_updated":"2021-01-12T08:19:41Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"None","month":"06","intvolume":"        28","language":[{"iso":"eng"}],"status":"public","abstract":[{"text":"In the present note we announce a proof of a strong form of Arnold diffusion for smooth convex Hamiltonian systems. Let ${\\mathbb T}^2$  be a 2-dimensional torus and B2 be the unit ball around the origin in ${\\mathbb R}^2$ . Fix ρ > 0. Our main result says that for a 'generic' time-periodic perturbation of an integrable system of two degrees of freedom $H_0(p)+\\varepsilon H_1(\\theta,p,t),\\quad \\ \\theta\\in {\\mathbb T}^2,\\ p\\in B^2,\\ t\\in {\\mathbb T}={\\mathbb R}/{\\mathbb Z}$ , with a strictly convex H0, there exists a ρ-dense orbit (θε, pε, t)(t) in ${\\mathbb T}^2 \\times B^2 \\times {\\mathbb T}$ , namely, a ρ-neighborhood of the orbit contains ${\\mathbb T}^2 \\times B^2 \\times {\\mathbb T}$ .\r\n\r\nOur proof is a combination of geometric and variational methods. The fundamental elements of the construction are the usage of crumpled normally hyperbolic invariant cylinders from [9], flower and simple normally hyperbolic invariant manifolds from [36] as well as their kissing property at a strong double resonance. This allows us to build a 'connected' net of three-dimensional normally hyperbolic invariant manifolds. To construct diffusing orbits along this net we employ a version of the Mather variational method [41] equipped with weak KAM theory [28], proposed by Bernard in [7].","lang":"eng"}],"publication":"Nonlinearity","volume":28,"publisher":"IOP Publishing","article_processing_charge":"No","_id":"8498","keyword":["Mathematical Physics","General Physics and Astronomy","Applied Mathematics","Statistical and Nonlinear Physics"],"quality_controlled":"1","issue":"8","date_published":"2015-06-30T00:00:00Z","title":"Arnold diffusion for smooth convex systems of two and a half degrees of freedom","author":[{"full_name":"Kaloshin, Vadim","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","last_name":"Kaloshin","first_name":"Vadim","orcid":"0000-0002-6051-2628"},{"full_name":"Zhang, K","last_name":"Zhang","first_name":"K"}],"year":"2015","publication_status":"published","extern":"1"},{"related_material":{"link":[{"relation":"erratum","url":"https://doi.org/10.1093/bioinformatics/btz397"}]},"page":"2219-2220","type":"journal_article","date_updated":"2021-01-12T08:19:25Z","doi":"10.1093/bioinformatics/btu166","date_created":"2020-09-18T10:08:07Z","month":"08","oa_version":"None","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_type":"original","day":"01","fulldoi":"https://doi.org/10.1093/bioinformatics/btu166","publication_identifier":{"issn":["1367-4803","1460-2059"]},"citation":{"ama":"Morin S, Linnet TE, Lescanne M, et al. Relax: The analysis of biomolecular kinetics and thermodynamics using NMR relaxation dispersion data. <i>Bioinformatics</i>. 2014;30(15):2219-2220. doi:<a href=\"https://doi.org/10.1093/bioinformatics/btu166\">10.1093/bioinformatics/btu166</a>","mla":"Morin, Sébastien, et al. “Relax: The Analysis of Biomolecular Kinetics and Thermodynamics Using NMR Relaxation Dispersion Data.” <i>Bioinformatics</i>, vol. 30, no. 15, Oxford University Press, 2014, pp. 2219–20, doi:<a href=\"https://doi.org/10.1093/bioinformatics/btu166\">10.1093/bioinformatics/btu166</a>.","apa":"Morin, S., Linnet, T. E., Lescanne, M., Schanda, P., Thompson, G. S., Tollinger, M., … d’Auvergne, E. J. (2014). Relax: The analysis of biomolecular kinetics and thermodynamics using NMR relaxation dispersion data. <i>Bioinformatics</i>. Oxford University Press. <a href=\"https://doi.org/10.1093/bioinformatics/btu166\">https://doi.org/10.1093/bioinformatics/btu166</a>","ieee":"S. Morin <i>et al.</i>, “Relax: The analysis of biomolecular kinetics and thermodynamics using NMR relaxation dispersion data,” <i>Bioinformatics</i>, vol. 30, no. 15. Oxford University Press, pp. 2219–2220, 2014.","short":"S. Morin, T.E. Linnet, M. Lescanne, P. Schanda, G.S. Thompson, M. Tollinger, K. Teilum, S. Gagné, D. Marion, C. Griesinger, M. Blackledge, E.J. d’Auvergne, Bioinformatics 30 (2014) 2219–2220.","ista":"Morin S, Linnet TE, Lescanne M, Schanda P, Thompson GS, Tollinger M, Teilum K, Gagné S, Marion D, Griesinger C, Blackledge M, d’Auvergne EJ. 2014. Relax: The analysis of biomolecular kinetics and thermodynamics using NMR relaxation dispersion data. Bioinformatics. 30(15), 2219–2220.","chicago":"Morin, Sébastien, Troels E Linnet, Mathilde Lescanne, Paul Schanda, Gary S Thompson, Martin Tollinger, Kaare Teilum, et al. “Relax: The Analysis of Biomolecular Kinetics and Thermodynamics Using NMR Relaxation Dispersion Data.” <i>Bioinformatics</i>. Oxford University Press, 2014. <a href=\"https://doi.org/10.1093/bioinformatics/btu166\">https://doi.org/10.1093/bioinformatics/btu166</a>."},"date_published":"2014-08-01T00:00:00Z","author":[{"last_name":"Morin","first_name":"Sébastien","full_name":"Morin, Sébastien"},{"first_name":"Troels E","last_name":"Linnet","full_name":"Linnet, Troels E"},{"last_name":"Lescanne","first_name":"Mathilde","full_name":"Lescanne, Mathilde"},{"last_name":"Schanda","first_name":"Paul","orcid":"0000-0002-9350-7606","full_name":"Schanda, Paul","id":"7B541462-FAF6-11E9-A490-E8DFE5697425"},{"full_name":"Thompson, Gary S","last_name":"Thompson","first_name":"Gary S"},{"full_name":"Tollinger, Martin","first_name":"Martin","last_name":"Tollinger"},{"full_name":"Teilum, Kaare","first_name":"Kaare","last_name":"Teilum"},{"last_name":"Gagné","first_name":"Stéphane","full_name":"Gagné, Stéphane"},{"last_name":"Marion","first_name":"Dominique","full_name":"Marion, Dominique"},{"full_name":"Griesinger, Christian","first_name":"Christian","last_name":"Griesinger"},{"full_name":"Blackledge, Martin","last_name":"Blackledge","first_name":"Martin"},{"last_name":"d’Auvergne","first_name":"Edward J","full_name":"d’Auvergne, Edward J"}],"title":"Relax: The analysis of biomolecular kinetics and thermodynamics using NMR relaxation dispersion data","extern":"1","publication_status":"published","year":"2014","abstract":[{"text":"Nuclear magnetic resonance (NMR) is a powerful tool for observing the motion of biomolecules at the atomic level. One technique, the analysis of relaxation dispersion phenomenon, is highly suited for studying the kinetics and thermodynamics of biological processes. Built on top of the relax computational environment for NMR dynamics is a new dispersion analysis designed to be comprehensive, accurate and easy-to-use. The software supports more models, both numeric and analytic, than current solutions. An automated protocol, available for scripting and driving the graphical user interface (GUI), is designed to simplify the analysis of dispersion data for NMR spectroscopists. Decreases in optimization time are granted by parallelization for running on computer clusters and by skipping an initial grid search by using parameters from one solution as the starting point for another —using analytic model results for the numeric models, taking advantage of model nesting, and using averaged non-clustered results for the clustered analysis.","lang":"eng"}],"intvolume":"        30","status":"public","language":[{"iso":"eng"}],"volume":30,"publication":"Bioinformatics","_id":"8459","publisher":"Oxford University Press","article_processing_charge":"No","issue":"15","keyword":["Statistics and Probability","Computational Theory and Mathematics","Biochemistry","Molecular Biology","Computational Mathematics","Computer Science Applications"],"quality_controlled":"1"},{"day":"01","article_type":"original","citation":{"mla":"Kaloshin, Vadim, et al. “Arnol′d Diffusion in a Pendulum Lattice.” <i>Communications on Pure and Applied Mathematics</i>, vol. 67, no. 5, Wiley, 2014, pp. 748–75, doi:<a href=\"https://doi.org/10.1002/cpa.21509\">10.1002/cpa.21509</a>.","apa":"Kaloshin, V., Levi, M., &#38; Saprykina, M. (2014). Arnol′d diffusion in a pendulum lattice. <i>Communications on Pure and Applied Mathematics</i>. Wiley. <a href=\"https://doi.org/10.1002/cpa.21509\">https://doi.org/10.1002/cpa.21509</a>","ieee":"V. Kaloshin, M. Levi, and M. Saprykina, “Arnol′d diffusion in a pendulum lattice,” <i>Communications on Pure and Applied Mathematics</i>, vol. 67, no. 5. Wiley, pp. 748–775, 2014.","ama":"Kaloshin V, Levi M, Saprykina M. Arnol′d diffusion in a pendulum lattice. <i>Communications on Pure and Applied Mathematics</i>. 2014;67(5):748-775. doi:<a href=\"https://doi.org/10.1002/cpa.21509\">10.1002/cpa.21509</a>","short":"V. Kaloshin, M. Levi, M. Saprykina, Communications on Pure and Applied Mathematics 67 (2014) 748–775.","chicago":"Kaloshin, Vadim, Mark Levi, and Maria Saprykina. “Arnol′d Diffusion in a Pendulum Lattice.” <i>Communications on Pure and Applied Mathematics</i>. Wiley, 2014. <a href=\"https://doi.org/10.1002/cpa.21509\">https://doi.org/10.1002/cpa.21509</a>.","ista":"Kaloshin V, Levi M, Saprykina M. 2014. Arnol′d diffusion in a pendulum lattice. Communications on Pure and Applied Mathematics. 67(5), 748–775."},"publication_identifier":{"issn":["0010-3640"]},"fulldoi":"https://doi.org/10.1002/cpa.21509","page":"748-775","type":"journal_article","date_updated":"2022-08-25T13:58:13Z","doi":"10.1002/cpa.21509","date_created":"2020-09-18T10:47:01Z","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","oa_version":"None","month":"05","status":"public","language":[{"iso":"eng"}],"intvolume":"        67","abstract":[{"text":"The main model studied in this paper is a lattice of pendula with a nearest‐neighbor coupling. If the coupling is weak, then the system is near‐integrable and KAM tori fill most of the phase space. For all KAM trajectories the energy of each pendulum stays within a narrow band for all time. Still, we show that for an arbitrarily weak coupling of a certain localized type, the neighboring pendula can exchange energy. In fact, the energy can be transferred between the pendula in any prescribed way.","lang":"eng"}],"publication":"Communications on Pure and Applied Mathematics","volume":67,"article_processing_charge":"No","publisher":"Wiley","_id":"8500","quality_controlled":"1","keyword":["Applied Mathematics","General Mathematics"],"issue":"5","date_published":"2014-05-01T00:00:00Z","author":[{"orcid":"0000-0002-6051-2628","first_name":"Vadim","last_name":"Kaloshin","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","full_name":"Kaloshin, Vadim"},{"full_name":"Levi, Mark","last_name":"Levi","first_name":"Mark"},{"last_name":"Saprykina","first_name":"Maria","full_name":"Saprykina, Maria"}],"title":"Arnol′d diffusion in a pendulum lattice","year":"2014","publication_status":"published","extern":"1"},{"author":[{"full_name":"Bounemoura, Abed","last_name":"Bounemoura","first_name":"Abed"},{"full_name":"Kaloshin, Vadim","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","last_name":"Kaloshin","first_name":"Vadim","orcid":"0000-0002-6051-2628"}],"title":"Generic fast diffusion for a class of non-convex Hamiltonians with two degrees of freedom","date_published":"2014-04-01T00:00:00Z","year":"2014","publication_status":"published","extern":"1","volume":14,"publication":"Moscow Mathematical Journal","abstract":[{"lang":"eng","text":"In this paper, we study small perturbations of a class of non-convex integrable Hamiltonians with two degrees of freedom, and we prove a result of diffusion for an open and dense set of perturbations, with an optimal time of diffusion which grows linearly with respect to the inverse of the size of the perturbation."}],"status":"public","language":[{"iso":"eng"}],"intvolume":"        14","keyword":["General Mathematics"],"quality_controlled":"1","issue":"2","external_id":{"arxiv":["1304.3050"]},"publisher":"Independent University of Moscow","article_processing_charge":"No","_id":"8501","type":"journal_article","page":"181-203","oa_version":"Preprint","arxiv":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","month":"04","date_updated":"2021-01-12T08:19:43Z","date_created":"2020-09-18T10:47:09Z","doi":"10.17323/1609-4514-2014-14-2-181-203","day":"01","article_type":"original","publication_identifier":{"issn":["1609-3321","1609-4514"]},"fulldoi":"https://doi.org/10.17323/1609-4514-2014-14-2-181-203","citation":{"ama":"Bounemoura A, Kaloshin V. Generic fast diffusion for a class of non-convex Hamiltonians with two degrees of freedom. <i>Moscow Mathematical Journal</i>. 2014;14(2):181-203. doi:<a href=\"https://doi.org/10.17323/1609-4514-2014-14-2-181-203\">10.17323/1609-4514-2014-14-2-181-203</a>","apa":"Bounemoura, A., &#38; Kaloshin, V. (2014). Generic fast diffusion for a class of non-convex Hamiltonians with two degrees of freedom. <i>Moscow Mathematical Journal</i>. Independent University of Moscow. <a href=\"https://doi.org/10.17323/1609-4514-2014-14-2-181-203\">https://doi.org/10.17323/1609-4514-2014-14-2-181-203</a>","ieee":"A. Bounemoura and V. Kaloshin, “Generic fast diffusion for a class of non-convex Hamiltonians with two degrees of freedom,” <i>Moscow Mathematical Journal</i>, vol. 14, no. 2. Independent University of Moscow, pp. 181–203, 2014.","mla":"Bounemoura, Abed, and Vadim Kaloshin. “Generic Fast Diffusion for a Class of Non-Convex Hamiltonians with Two Degrees of Freedom.” <i>Moscow Mathematical Journal</i>, vol. 14, no. 2, Independent University of Moscow, 2014, pp. 181–203, doi:<a href=\"https://doi.org/10.17323/1609-4514-2014-14-2-181-203\">10.17323/1609-4514-2014-14-2-181-203</a>.","short":"A. Bounemoura, V. Kaloshin, Moscow Mathematical Journal 14 (2014) 181–203.","ista":"Bounemoura A, Kaloshin V. 2014. Generic fast diffusion for a class of non-convex Hamiltonians with two degrees of freedom. Moscow Mathematical Journal. 14(2), 181–203.","chicago":"Bounemoura, Abed, and Vadim Kaloshin. “Generic Fast Diffusion for a Class of Non-Convex Hamiltonians with Two Degrees of Freedom.” <i>Moscow Mathematical Journal</i>. Independent University of Moscow, 2014. <a href=\"https://doi.org/10.17323/1609-4514-2014-14-2-181-203\">https://doi.org/10.17323/1609-4514-2014-14-2-181-203</a>."}},{"author":[{"last_name":"Palacci","orcid":"0000-0002-7253-9465","first_name":"Jérémie A","id":"8fb92548-2b22-11eb-b7c1-a3f0d08d7c7d","full_name":"Palacci, Jérémie A"},{"full_name":"Sacanna, S.","first_name":"S.","last_name":"Sacanna"},{"first_name":"S.-H.","last_name":"Kim","full_name":"Kim, S.-H."},{"first_name":"G.-R.","last_name":"Yi","full_name":"Yi, G.-R."},{"full_name":"Pine, D. J.","last_name":"Pine","first_name":"D. J."},{"last_name":"Chaikin","first_name":"P. M.","full_name":"Chaikin, P. M."}],"title":"Light-activated self-propelled colloids","date_published":"2014-11-28T00:00:00Z","year":"2014","publication_status":"published","extern":"1","volume":372,"publication":"Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences","abstract":[{"lang":"eng","text":"Light-activated self-propelled colloids are synthesized and their active motion is studied using optical microscopy. We propose a versatile route using different photoactive materials, and demonstrate a multiwavelength activation and propulsion. Thanks to the photoelectrochemical properties of two semiconductor materials (α-Fe2O3 and TiO2), a light with an energy higher than the bandgap triggers the reaction of decomposition of hydrogen peroxide and produces a chemical cloud around the particle. It induces a phoretic attraction with neighbouring colloids as well as an osmotic self-propulsion of the particle on the substrate. We use these mechanisms to form colloidal cargos as well as self-propelled particles where the light-activated component is embedded into a dielectric sphere. The particles are self-propelled along a direction otherwise randomized by thermal fluctuations, and exhibit a persistent random walk. For sufficient surface density, the particles spontaneously form ‘living crystals’ which are mobile, break apart and reform. Steering the particle with an external magnetic field, we show that the formation of the dense phase results from the collisions heads-on of the particles. This effect is intrinsically non-equilibrium and a novel principle of organization for systems without detailed balance. Engineering families of particles self-propelled by different wavelength demonstrate a good understanding of both the physics and the chemistry behind the system and points to a general route for designing new families of self-propelled particles."}],"intvolume":"       372","language":[{"iso":"eng"}],"status":"public","keyword":["General Engineering","General Physics and Astronomy","General Mathematics"],"quality_controlled":"1","issue":"2029","article_number":"20130372","external_id":{"arxiv":["1410.7278"],"pmid":["25332383"]},"publisher":"The Royal Society","article_processing_charge":"No","_id":"9166","type":"journal_article","pmid":1,"oa_version":"Published Version","arxiv":1,"user_id":"D865714E-FA4E-11E9-B85B-F5C5E5697425","month":"11","date_updated":"2021-02-22T10:44:16Z","doi":"10.1098/rsta.2013.0372","date_created":"2021-02-18T14:31:11Z","day":"28","article_type":"original","fulldoi":"https://doi.org/10.1098/rsta.2013.0372","citation":{"ama":"Palacci JA, Sacanna S, Kim S-H, Yi G-R, Pine DJ, Chaikin PM. Light-activated self-propelled colloids. <i>Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences</i>. 2014;372(2029). doi:<a href=\"https://doi.org/10.1098/rsta.2013.0372\">10.1098/rsta.2013.0372</a>","ieee":"J. A. Palacci, S. Sacanna, S.-H. Kim, G.-R. Yi, D. J. Pine, and P. M. Chaikin, “Light-activated self-propelled colloids,” <i>Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences</i>, vol. 372, no. 2029. The Royal Society, 2014.","apa":"Palacci, J. A., Sacanna, S., Kim, S.-H., Yi, G.-R., Pine, D. J., &#38; Chaikin, P. M. (2014). Light-activated self-propelled colloids. <i>Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences</i>. The Royal Society. <a href=\"https://doi.org/10.1098/rsta.2013.0372\">https://doi.org/10.1098/rsta.2013.0372</a>","mla":"Palacci, Jérémie A., et al. “Light-Activated Self-Propelled Colloids.” <i>Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences</i>, vol. 372, no. 2029, 20130372, The Royal Society, 2014, doi:<a href=\"https://doi.org/10.1098/rsta.2013.0372\">10.1098/rsta.2013.0372</a>.","ista":"Palacci JA, Sacanna S, Kim S-H, Yi G-R, Pine DJ, Chaikin PM. 2014. Light-activated self-propelled colloids. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. 372(2029), 20130372.","chicago":"Palacci, Jérémie A, S. Sacanna, S.-H. Kim, G.-R. Yi, D. J. Pine, and P. M. Chaikin. “Light-Activated Self-Propelled Colloids.” <i>Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences</i>. The Royal Society, 2014. <a href=\"https://doi.org/10.1098/rsta.2013.0372\">https://doi.org/10.1098/rsta.2013.0372</a>.","short":"J.A. Palacci, S. Sacanna, S.-H. Kim, G.-R. Yi, D.J. Pine, P.M. Chaikin, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 372 (2014)."},"publication_identifier":{"eissn":["1471-2962"],"issn":["1364-503X"]},"main_file_link":[{"url":"https://doi.org/10.1098/rsta.2013.0372","open_access":"1"}],"oa":1,"scopus_import":"1"},{"day":"01","article_type":"original","citation":{"short":"V. Kaloshin, O.S. KOZLOVSKI, Ergodic Theory and Dynamical Systems 32 (2012) 159–165.","ista":"Kaloshin V, KOZLOVSKI OS. 2012. A Cr unimodal map with an arbitrary fast growth of the number of periodic points. Ergodic Theory and Dynamical Systems. 32(1), 159–165.","chicago":"Kaloshin, Vadim, and O. S. KOZLOVSKI. “A Cr Unimodal Map with an Arbitrary Fast Growth of the Number of Periodic Points.” <i>Ergodic Theory and Dynamical Systems</i>. Cambridge University Press, 2012. <a href=\"https://doi.org/10.1017/s0143385710000817\">https://doi.org/10.1017/s0143385710000817</a>.","ama":"Kaloshin V, KOZLOVSKI OS. A Cr unimodal map with an arbitrary fast growth of the number of periodic points. <i>Ergodic Theory and Dynamical Systems</i>. 2012;32(1):159-165. doi:<a href=\"https://doi.org/10.1017/s0143385710000817\">10.1017/s0143385710000817</a>","mla":"Kaloshin, Vadim, and O. S. KOZLOVSKI. “A Cr Unimodal Map with an Arbitrary Fast Growth of the Number of Periodic Points.” <i>Ergodic Theory and Dynamical Systems</i>, vol. 32, no. 1, Cambridge University Press, 2012, pp. 159–65, doi:<a href=\"https://doi.org/10.1017/s0143385710000817\">10.1017/s0143385710000817</a>.","ieee":"V. Kaloshin and O. S. KOZLOVSKI, “A Cr unimodal map with an arbitrary fast growth of the number of periodic points,” <i>Ergodic Theory and Dynamical Systems</i>, vol. 32, no. 1. Cambridge University Press, pp. 159–165, 2012.","apa":"Kaloshin, V., &#38; KOZLOVSKI, O. S. (2012). A Cr unimodal map with an arbitrary fast growth of the number of periodic points. <i>Ergodic Theory and Dynamical Systems</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/s0143385710000817\">https://doi.org/10.1017/s0143385710000817</a>"},"publication_identifier":{"issn":["0143-3857","1469-4417"]},"fulldoi":"https://doi.org/10.1017/s0143385710000817","page":"159-165","type":"journal_article","date_updated":"2021-01-12T08:19:44Z","doi":"10.1017/s0143385710000817","date_created":"2020-09-18T10:47:33Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"None","month":"02","status":"public","language":[{"iso":"eng"}],"intvolume":"        32","abstract":[{"lang":"eng","text":"In this paper we present a surprising example of a Cr unimodal map of an interval f:I→I whose number of periodic points Pn(f)=∣{x∈I:fnx=x}∣ grows faster than any ahead given sequence along a subsequence nk=3k. This example also shows that ‘non-flatness’ of critical points is necessary for the Martens–de Melo–van Strien theorem [M. Martens, W. de Melo and S. van Strien. Julia–Fatou–Sullivan theory for real one-dimensional dynamics. Acta Math.168(3–4) (1992), 273–318] to hold."}],"publication":"Ergodic Theory and Dynamical Systems","volume":32,"article_processing_charge":"No","publisher":"Cambridge University Press","_id":"8504","quality_controlled":"1","keyword":["Applied Mathematics","General Mathematics"],"issue":"1","date_published":"2012-02-01T00:00:00Z","title":"A Cr unimodal map with an arbitrary fast growth of the number of periodic points","author":[{"first_name":"Vadim","orcid":"0000-0002-6051-2628","last_name":"Kaloshin","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","full_name":"Kaloshin, Vadim"},{"full_name":"KOZLOVSKI, O. S.","last_name":"KOZLOVSKI","first_name":"O. S."}],"year":"2012","extern":"1","publication_status":"published"},{"citation":{"ama":"Galante J, Kaloshin V. Destruction of invariant curves in the restricted circular planar three-body problem by using comparison of action. <i>Duke Mathematical Journal</i>. 2011;159(2):275-327. doi:<a href=\"https://doi.org/10.1215/00127094-1415878\">10.1215/00127094-1415878</a>","apa":"Galante, J., &#38; Kaloshin, V. (2011). Destruction of invariant curves in the restricted circular planar three-body problem by using comparison of action. <i>Duke Mathematical Journal</i>. Duke University Press. <a href=\"https://doi.org/10.1215/00127094-1415878\">https://doi.org/10.1215/00127094-1415878</a>","ieee":"J. Galante and V. Kaloshin, “Destruction of invariant curves in the restricted circular planar three-body problem by using comparison of action,” <i>Duke Mathematical Journal</i>, vol. 159, no. 2. Duke University Press, pp. 275–327, 2011.","mla":"Galante, Joseph, and Vadim Kaloshin. “Destruction of Invariant Curves in the Restricted Circular Planar Three-Body Problem by Using Comparison of Action.” <i>Duke Mathematical Journal</i>, vol. 159, no. 2, Duke University Press, 2011, pp. 275–327, doi:<a href=\"https://doi.org/10.1215/00127094-1415878\">10.1215/00127094-1415878</a>.","short":"J. Galante, V. Kaloshin, Duke Mathematical Journal 159 (2011) 275–327.","ista":"Galante J, Kaloshin V. 2011. Destruction of invariant curves in the restricted circular planar three-body problem by using comparison of action. Duke Mathematical Journal. 159(2), 275–327.","chicago":"Galante, Joseph, and Vadim Kaloshin. “Destruction of Invariant Curves in the Restricted Circular Planar Three-Body Problem by Using Comparison of Action.” <i>Duke Mathematical Journal</i>. Duke University Press, 2011. <a href=\"https://doi.org/10.1215/00127094-1415878\">https://doi.org/10.1215/00127094-1415878</a>."},"publication_identifier":{"issn":["0012-7094"]},"fulldoi":"https://doi.org/10.1215/00127094-1415878","article_type":"original","day":"04","doi":"10.1215/00127094-1415878","date_updated":"2021-01-12T08:19:45Z","date_created":"2020-09-18T10:47:41Z","month":"08","oa_version":"None","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","page":"275-327","type":"journal_article","_id":"8505","publisher":"Duke University Press","article_processing_charge":"No","issue":"2","quality_controlled":"1","keyword":["General Mathematics"],"abstract":[{"lang":"eng","text":"The classical principle of least action says that orbits of mechanical systems extremize action; an important subclass are those orbits that minimize action. In this paper we utilize this principle along with Aubry-Mather theory to construct (Birkhoff) regions of instability for a certain three-body problem, given by a Hamiltonian system of 2 degrees of freedom. We believe that these methods can be applied to construct instability regions for a variety of Hamiltonian systems with 2 degrees of freedom. The Hamiltonian model we consider describes dynamics of a Sun-Jupiter-comet system, and under some simplifying assumptions, we show the existence of instabilities for the orbit of the comet. In particular, we show that a comet which starts close to an orbit in the shape of an ellipse of eccentricity e=0.66 can increase in eccentricity up to e=0.96. In the sequels to this paper, we extend the result to beyond e=1 and show the existence of ejection orbits. Such orbits are initially well within the range of our solar system. This might give an indication of why most objects rotating around the Sun in our solar system have relatively low eccentricity."}],"intvolume":"       159","language":[{"iso":"eng"}],"status":"public","volume":159,"publication":"Duke Mathematical Journal","publication_status":"published","extern":"1","year":"2011","date_published":"2011-08-04T00:00:00Z","title":"Destruction of invariant curves in the restricted circular planar three-body problem by using comparison of action","author":[{"first_name":"Joseph","last_name":"Galante","full_name":"Galante, Joseph"},{"id":"FE553552-CDE8-11E9-B324-C0EBE5697425","full_name":"Kaloshin, Vadim","orcid":"0000-0002-6051-2628","first_name":"Vadim","last_name":"Kaloshin"}]},{"keyword":["Mathematics (miscellaneous)"],"quality_controlled":"1","issue":"1","publisher":"Springer Nature","article_processing_charge":"No","_id":"8508","volume":267,"publication":"Proceedings of the Steklov Institute of Mathematics","abstract":[{"text":"We study generic unfoldings of homoclinic tangencies of two-dimensional area-preserving diffeomorphisms (conservative New house phenomena) and show that they give rise to invariant hyperbolic sets of arbitrarily large Hausdorff dimension. As applications, we discuss the size of the stochastic layer of a standard map and the Hausdorff dimension of invariant hyperbolic sets for certain restricted three-body problems. We avoid involved technical details and only concentrate on the ideas of the proof of the presented results.","lang":"eng"}],"language":[{"iso":"eng"}],"intvolume":"       267","status":"public","year":"2009","publication_status":"published","extern":"1","title":"Conservative homoclinic bifurcations and some applications","author":[{"full_name":"Gorodetski, Anton","first_name":"Anton","last_name":"Gorodetski"},{"id":"FE553552-CDE8-11E9-B324-C0EBE5697425","full_name":"Kaloshin, Vadim","last_name":"Kaloshin","orcid":"0000-0002-6051-2628","first_name":"Vadim"}],"date_published":"2009-12-01T00:00:00Z","publication_identifier":{"issn":["0081-5438","1531-8605"]},"citation":{"short":"A. Gorodetski, V. Kaloshin, Proceedings of the Steklov Institute of Mathematics 267 (2009) 76–90.","chicago":"Gorodetski, Anton, and Vadim Kaloshin. “Conservative Homoclinic Bifurcations and Some Applications.” <i>Proceedings of the Steklov Institute of Mathematics</i>. Springer Nature, 2009. <a href=\"https://doi.org/10.1134/s0081543809040063\">https://doi.org/10.1134/s0081543809040063</a>.","ista":"Gorodetski A, Kaloshin V. 2009. Conservative homoclinic bifurcations and some applications. Proceedings of the Steklov Institute of Mathematics. 267(1), 76–90.","mla":"Gorodetski, Anton, and Vadim Kaloshin. “Conservative Homoclinic Bifurcations and Some Applications.” <i>Proceedings of the Steklov Institute of Mathematics</i>, vol. 267, no. 1, Springer Nature, 2009, pp. 76–90, doi:<a href=\"https://doi.org/10.1134/s0081543809040063\">10.1134/s0081543809040063</a>.","apa":"Gorodetski, A., &#38; Kaloshin, V. (2009). Conservative homoclinic bifurcations and some applications. <i>Proceedings of the Steklov Institute of Mathematics</i>. Springer Nature. <a href=\"https://doi.org/10.1134/s0081543809040063\">https://doi.org/10.1134/s0081543809040063</a>","ieee":"A. Gorodetski and V. Kaloshin, “Conservative homoclinic bifurcations and some applications,” <i>Proceedings of the Steklov Institute of Mathematics</i>, vol. 267, no. 1. Springer Nature, pp. 76–90, 2009.","ama":"Gorodetski A, Kaloshin V. Conservative homoclinic bifurcations and some applications. <i>Proceedings of the Steklov Institute of Mathematics</i>. 2009;267(1):76-90. doi:<a href=\"https://doi.org/10.1134/s0081543809040063\">10.1134/s0081543809040063</a>"},"fulldoi":"https://doi.org/10.1134/s0081543809040063","day":"01","article_type":"original","oa_version":"None","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","month":"12","doi":"10.1134/s0081543809040063","date_updated":"2021-01-12T08:19:46Z","date_created":"2020-09-18T10:48:03Z","type":"journal_article","page":"76-90"},{"article_type":"original","day":"05","publication_identifier":{"issn":["0036-1445","1095-7200"]},"fulldoi":"https://doi.org/10.1137/070703235","citation":{"short":"V. Kaloshin, M. Levi, SIAM Review 50 (2008) 702–720.","chicago":"Kaloshin, Vadim, and Mark Levi. “Geometry of Arnold Diffusion.” <i>SIAM Review</i>. Society for Industrial &#38; Applied Mathematics, 2008. <a href=\"https://doi.org/10.1137/070703235\">https://doi.org/10.1137/070703235</a>.","ista":"Kaloshin V, Levi M. 2008. Geometry of Arnold diffusion. SIAM Review. 50(4), 702–720.","mla":"Kaloshin, Vadim, and Mark Levi. “Geometry of Arnold Diffusion.” <i>SIAM Review</i>, vol. 50, no. 4, Society for Industrial &#38; Applied Mathematics, 2008, pp. 702–20, doi:<a href=\"https://doi.org/10.1137/070703235\">10.1137/070703235</a>.","ieee":"V. Kaloshin and M. Levi, “Geometry of Arnold diffusion,” <i>SIAM Review</i>, vol. 50, no. 4. Society for Industrial &#38; Applied Mathematics, pp. 702–720, 2008.","apa":"Kaloshin, V., &#38; Levi, M. (2008). Geometry of Arnold diffusion. <i>SIAM Review</i>. Society for Industrial &#38; Applied Mathematics. <a href=\"https://doi.org/10.1137/070703235\">https://doi.org/10.1137/070703235</a>","ama":"Kaloshin V, Levi M. Geometry of Arnold diffusion. <i>SIAM Review</i>. 2008;50(4):702-720. doi:<a href=\"https://doi.org/10.1137/070703235\">10.1137/070703235</a>"},"type":"journal_article","page":"702-720","month":"11","oa_version":"None","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","doi":"10.1137/070703235","date_created":"2020-09-18T10:48:12Z","date_updated":"2021-01-12T08:19:46Z","volume":50,"publication":"SIAM Review","abstract":[{"text":"The goal of this paper is to present to nonspecialists what is perhaps the simplest possible geometrical picture explaining the mechanism of Arnold diffusion. We choose to speak of a specific model—that of geometric rays in a periodic optical medium. This model is equivalent to that of a particle in a periodic potential in ${\\mathbb R}^{n}$ with energy prescribed and to the geodesic flow in a Riemannian metric on ${\\mathbb R}^{n} $.","lang":"eng"}],"language":[{"iso":"eng"}],"status":"public","intvolume":"        50","issue":"4","keyword":["Theoretical Computer Science","Applied Mathematics","Computational Mathematics"],"quality_controlled":"1","_id":"8509","publisher":"Society for Industrial & Applied Mathematics","article_processing_charge":"No","title":"Geometry of Arnold diffusion","author":[{"first_name":"Vadim","orcid":"0000-0002-6051-2628","last_name":"Kaloshin","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","full_name":"Kaloshin, Vadim"},{"last_name":"Levi","first_name":"Mark","full_name":"Levi, Mark"}],"date_published":"2008-11-05T00:00:00Z","extern":"1","publication_status":"published","year":"2008"},{"page":"409-427","type":"journal_article","date_created":"2020-09-18T10:48:20Z","date_updated":"2021-01-12T08:19:47Z","doi":"10.1090/s0273-0979-08-01211-1","month":"07","oa_version":"None","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_type":"original","day":"01","citation":{"apa":"Kaloshin, V., &#38; Levi, M. (2008). An example of Arnold diffusion for near-integrable Hamiltonians. <i>Bulletin of the American Mathematical Society</i>. American Mathematical Society. <a href=\"https://doi.org/10.1090/s0273-0979-08-01211-1\">https://doi.org/10.1090/s0273-0979-08-01211-1</a>","mla":"Kaloshin, Vadim, and Mark Levi. “An Example of Arnold Diffusion for Near-Integrable Hamiltonians.” <i>Bulletin of the American Mathematical Society</i>, vol. 45, no. 3, American Mathematical Society, 2008, pp. 409–27, doi:<a href=\"https://doi.org/10.1090/s0273-0979-08-01211-1\">10.1090/s0273-0979-08-01211-1</a>.","ieee":"V. Kaloshin and M. Levi, “An example of Arnold diffusion for near-integrable Hamiltonians,” <i>Bulletin of the American Mathematical Society</i>, vol. 45, no. 3. American Mathematical Society, pp. 409–427, 2008.","ama":"Kaloshin V, Levi M. An example of Arnold diffusion for near-integrable Hamiltonians. <i>Bulletin of the American Mathematical Society</i>. 2008;45(3):409-427. doi:<a href=\"https://doi.org/10.1090/s0273-0979-08-01211-1\">10.1090/s0273-0979-08-01211-1</a>","short":"V. Kaloshin, M. Levi, Bulletin of the American Mathematical Society 45 (2008) 409–427.","chicago":"Kaloshin, Vadim, and Mark Levi. “An Example of Arnold Diffusion for Near-Integrable Hamiltonians.” <i>Bulletin of the American Mathematical Society</i>. American Mathematical Society, 2008. <a href=\"https://doi.org/10.1090/s0273-0979-08-01211-1\">https://doi.org/10.1090/s0273-0979-08-01211-1</a>.","ista":"Kaloshin V, Levi M. 2008. An example of Arnold diffusion for near-integrable Hamiltonians. Bulletin of the American Mathematical Society. 45(3), 409–427."},"fulldoi":"https://doi.org/10.1090/s0273-0979-08-01211-1","publication_identifier":{"issn":["0273-0979"]},"date_published":"2008-07-01T00:00:00Z","author":[{"first_name":"Vadim","orcid":"0000-0002-6051-2628","last_name":"Kaloshin","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","full_name":"Kaloshin, Vadim"},{"last_name":"Levi","first_name":"Mark","full_name":"Levi, Mark"}],"title":"An example of Arnold diffusion for near-integrable Hamiltonians","publication_status":"published","extern":"1","year":"2008","abstract":[{"text":"In this paper, using the ideas of Bessi and Mather, we present a simple mechanical system exhibiting Arnold diffusion. This system of a particle in a small periodic potential can be also interpreted as ray propagation in a periodic optical medium with a near-constant index of refraction. Arnold diffusion in this context manifests itself as an arbitrary finite change of direction for nearly constant index of refraction.","lang":"eng"}],"status":"public","intvolume":"        45","language":[{"iso":"eng"}],"volume":45,"publication":"Bulletin of the American Mathematical Society","_id":"8510","publisher":"American Mathematical Society","article_processing_charge":"No","issue":"3","keyword":["Applied Mathematics","General Mathematics"],"quality_controlled":"1"},{"date_published":"2007-01-30T00:00:00Z","title":"How often surface diffeomorphisms have infinitely many sinks and hyperbolicity of periodic points near a homoclinic tangency","author":[{"first_name":"A.","last_name":"Gorodetski","full_name":"Gorodetski, A."},{"id":"FE553552-CDE8-11E9-B324-C0EBE5697425","full_name":"Kaloshin, Vadim","first_name":"Vadim","orcid":"0000-0002-6051-2628","last_name":"Kaloshin"}],"year":"2007","extern":"1","publication_status":"published","language":[{"iso":"eng"}],"status":"public","intvolume":"       208","abstract":[{"text":"Here we study an amazing phenomenon discovered by Newhouse [S. Newhouse, Non-density of Axiom A(a) on S2, in: Proc. Sympos. Pure Math., vol. 14, Amer. Math. Soc., 1970, pp. 191–202; S. Newhouse,\r\nDiffeomorphisms with infinitely many sinks, Topology 13 (1974) 9–18; S. Newhouse, The abundance of\r\nwild hyperbolic sets and nonsmooth stable sets of diffeomorphisms, Publ. Math. Inst. Hautes Études Sci.\r\n50 (1979) 101–151]. It turns out that in the space of Cr smooth diffeomorphisms Diffr(M) of a compact\r\nsurface M there is an open set U such that a Baire generic diffeomorphism f ∈ U has infinitely many coexisting sinks. In this paper we make a step towards understanding “how often does a surface diffeomorphism\r\nhave infinitely many sinks.” Our main result roughly says that with probability one for any positive D a\r\nsurface diffeomorphism has only finitely many localized sinks either of cyclicity bounded by D or those\r\nwhose period is relatively large compared to its cyclicity. It verifies a particular case of Palis’ Conjecture\r\nsaying that even though diffeomorphisms with infinitely many coexisting sinks are Baire generic, they have\r\nprobability zero.\r\nOne of the key points of the proof is an application of Newton Interpolation Polynomials to study the dynamics initiated in [V. Kaloshin, B. Hunt, A stretched exponential bound on the rate of growth of the number\r\nof periodic points for prevalent diffeomorphisms I, Ann. of Math., in press, 92 pp.; V. Kaloshin, A stretched\r\nexponential bound on the rate of growth of the number of periodic points for prevalent diffeomorphisms II,\r\npreprint, 85 pp.].","lang":"eng"}],"publication":"Advances in Mathematics","volume":208,"publisher":"Elsevier","article_processing_charge":"No","_id":"8511","keyword":["General Mathematics"],"quality_controlled":"1","issue":"2","page":"710-797","type":"journal_article","doi":"10.1016/j.aim.2006.03.012","date_created":"2020-09-18T10:48:27Z","date_updated":"2021-01-12T08:19:47Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"None","month":"01","day":"30","article_type":"original","fulldoi":"https://doi.org/10.1016/j.aim.2006.03.012","citation":{"ieee":"A. Gorodetski and V. Kaloshin, “How often surface diffeomorphisms have infinitely many sinks and hyperbolicity of periodic points near a homoclinic tangency,” <i>Advances in Mathematics</i>, vol. 208, no. 2. Elsevier, pp. 710–797, 2007.","mla":"Gorodetski, A., and Vadim Kaloshin. “How Often Surface Diffeomorphisms Have Infinitely Many Sinks and Hyperbolicity of Periodic Points near a Homoclinic Tangency.” <i>Advances in Mathematics</i>, vol. 208, no. 2, Elsevier, 2007, pp. 710–97, doi:<a href=\"https://doi.org/10.1016/j.aim.2006.03.012\">10.1016/j.aim.2006.03.012</a>.","apa":"Gorodetski, A., &#38; Kaloshin, V. (2007). How often surface diffeomorphisms have infinitely many sinks and hyperbolicity of periodic points near a homoclinic tangency. <i>Advances in Mathematics</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.aim.2006.03.012\">https://doi.org/10.1016/j.aim.2006.03.012</a>","ama":"Gorodetski A, Kaloshin V. How often surface diffeomorphisms have infinitely many sinks and hyperbolicity of periodic points near a homoclinic tangency. <i>Advances in Mathematics</i>. 2007;208(2):710-797. doi:<a href=\"https://doi.org/10.1016/j.aim.2006.03.012\">10.1016/j.aim.2006.03.012</a>","chicago":"Gorodetski, A., and Vadim Kaloshin. “How Often Surface Diffeomorphisms Have Infinitely Many Sinks and Hyperbolicity of Periodic Points near a Homoclinic Tangency.” <i>Advances in Mathematics</i>. Elsevier, 2007. <a href=\"https://doi.org/10.1016/j.aim.2006.03.012\">https://doi.org/10.1016/j.aim.2006.03.012</a>.","ista":"Gorodetski A, Kaloshin V. 2007. How often surface diffeomorphisms have infinitely many sinks and hyperbolicity of periodic points near a homoclinic tangency. Advances in Mathematics. 208(2), 710–797.","short":"A. Gorodetski, V. Kaloshin, Advances in Mathematics 208 (2007) 710–797."},"publication_identifier":{"issn":["0001-8708"]}},{"_id":"8517","publisher":"Wiley","article_processing_charge":"No","issue":"9","keyword":["Applied Mathematics","General Mathematics"],"quality_controlled":"1","abstract":[{"text":"We consider the evolution of a connected set on the plane carried by a space periodic incompressible stochastic flow. While for almost every realization of the stochastic flow at time t most of the particles are at a distance of order equation image away from the origin, there is a measure zero set of points that escape to infinity at the linear rate. We study the set of points visited by the original set by time t and show that such a set, when scaled down by the factor of t, has a limiting nonrandom shape.","lang":"eng"}],"status":"public","language":[{"iso":"eng"}],"intvolume":"        57","volume":57,"publication":"Communications on Pure and Applied Mathematics","extern":"1","publication_status":"published","year":"2004","date_published":"2004-09-01T00:00:00Z","title":"A limit shape theorem for periodic stochastic dispersion","author":[{"full_name":"Dolgopyat, Dmitry","last_name":"Dolgopyat","first_name":"Dmitry"},{"id":"FE553552-CDE8-11E9-B324-C0EBE5697425","full_name":"Kaloshin, Vadim","last_name":"Kaloshin","first_name":"Vadim","orcid":"0000-0002-6051-2628"},{"last_name":"Koralov","first_name":"Leonid","full_name":"Koralov, Leonid"}],"publication_identifier":{"issn":["0010-3640","1097-0312"]},"citation":{"ama":"Dolgopyat D, Kaloshin V, Koralov L. A limit shape theorem for periodic stochastic dispersion. <i>Communications on Pure and Applied Mathematics</i>. 2004;57(9):1127-1158. doi:<a href=\"https://doi.org/10.1002/cpa.20032\">10.1002/cpa.20032</a>","mla":"Dolgopyat, Dmitry, et al. “A Limit Shape Theorem for Periodic Stochastic Dispersion.” <i>Communications on Pure and Applied Mathematics</i>, vol. 57, no. 9, Wiley, 2004, pp. 1127–58, doi:<a href=\"https://doi.org/10.1002/cpa.20032\">10.1002/cpa.20032</a>.","apa":"Dolgopyat, D., Kaloshin, V., &#38; Koralov, L. (2004). A limit shape theorem for periodic stochastic dispersion. <i>Communications on Pure and Applied Mathematics</i>. Wiley. <a href=\"https://doi.org/10.1002/cpa.20032\">https://doi.org/10.1002/cpa.20032</a>","ieee":"D. Dolgopyat, V. Kaloshin, and L. Koralov, “A limit shape theorem for periodic stochastic dispersion,” <i>Communications on Pure and Applied Mathematics</i>, vol. 57, no. 9. Wiley, pp. 1127–1158, 2004.","short":"D. Dolgopyat, V. Kaloshin, L. Koralov, Communications on Pure and Applied Mathematics 57 (2004) 1127–1158.","ista":"Dolgopyat D, Kaloshin V, Koralov L. 2004. A limit shape theorem for periodic stochastic dispersion. Communications on Pure and Applied Mathematics. 57(9), 1127–1158.","chicago":"Dolgopyat, Dmitry, Vadim Kaloshin, and Leonid Koralov. “A Limit Shape Theorem for Periodic Stochastic Dispersion.” <i>Communications on Pure and Applied Mathematics</i>. Wiley, 2004. <a href=\"https://doi.org/10.1002/cpa.20032\">https://doi.org/10.1002/cpa.20032</a>."},"fulldoi":"https://doi.org/10.1002/cpa.20032","article_type":"original","day":"01","date_updated":"2021-01-12T08:19:50Z","date_created":"2020-09-18T10:49:12Z","doi":"10.1002/cpa.20032","month":"09","oa_version":"None","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","page":"1127-1158","type":"journal_article"},{"day":"01","publication":"Inventiones mathematicae","volume":151,"article_type":"original","language":[{"iso":"eng"}],"status":"public","intvolume":"       151","quality_controlled":"1","keyword":["General Mathematics"],"citation":{"chicago":"Kaloshin, Vadim. “The Existential Hilbert 16-Th Problem and an Estimate for Cyclicity of Elementary Polycycles.” <i>Inventiones Mathematicae</i>. Springer Nature, 2003. <a href=\"https://doi.org/10.1007/s00222-002-0244-9\">https://doi.org/10.1007/s00222-002-0244-9</a>.","ista":"Kaloshin V. 2003. The existential Hilbert 16-th problem and an estimate for cyclicity of elementary polycycles. Inventiones mathematicae. 151(3), 451–512.","short":"V. Kaloshin, Inventiones Mathematicae 151 (2003) 451–512.","mla":"Kaloshin, Vadim. “The Existential Hilbert 16-Th Problem and an Estimate for Cyclicity of Elementary Polycycles.” <i>Inventiones Mathematicae</i>, vol. 151, no. 3, Springer Nature, 2003, pp. 451–512, doi:<a href=\"https://doi.org/10.1007/s00222-002-0244-9\">10.1007/s00222-002-0244-9</a>.","apa":"Kaloshin, V. (2003). The existential Hilbert 16-th problem and an estimate for cyclicity of elementary polycycles. <i>Inventiones Mathematicae</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00222-002-0244-9\">https://doi.org/10.1007/s00222-002-0244-9</a>","ieee":"V. Kaloshin, “The existential Hilbert 16-th problem and an estimate for cyclicity of elementary polycycles,” <i>Inventiones mathematicae</i>, vol. 151, no. 3. Springer Nature, pp. 451–512, 2003.","ama":"Kaloshin V. The existential Hilbert 16-th problem and an estimate for cyclicity of elementary polycycles. <i>Inventiones mathematicae</i>. 2003;151(3):451-512. doi:<a href=\"https://doi.org/10.1007/s00222-002-0244-9\">10.1007/s00222-002-0244-9</a>"},"fulldoi":"https://doi.org/10.1007/s00222-002-0244-9","publication_identifier":{"issn":["0020-9910","1432-1297"]},"issue":"3","article_processing_charge":"No","publisher":"Springer Nature","_id":"8519","type":"journal_article","title":"The existential Hilbert 16-th problem and an estimate for cyclicity of elementary polycycles","author":[{"id":"FE553552-CDE8-11E9-B324-C0EBE5697425","full_name":"Kaloshin, Vadim","orcid":"0000-0002-6051-2628","first_name":"Vadim","last_name":"Kaloshin"}],"page":"451-512","date_published":"2003-03-01T00:00:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2003","oa_version":"None","month":"03","extern":"1","publication_status":"published","date_updated":"2021-01-12T08:19:50Z","doi":"10.1007/s00222-002-0244-9","date_created":"2020-09-18T10:49:26Z"},{"publication_identifier":{"issn":["1079-6762"]},"citation":{"mla":"Kaloshin, Vadim, and Brian R. Hunt. “A Stretched Exponential Bound on the Rate of Growth of the Number of Periodic Points for Prevalent Diffeomorphisms II.” <i>Electronic Research Announcements of the American Mathematical Society</i>, vol. 7, no. 5, American Mathematical Society, 2001, pp. 28–36, doi:<a href=\"https://doi.org/10.1090/s1079-6762-01-00091-9\">10.1090/s1079-6762-01-00091-9</a>.","ieee":"V. Kaloshin and B. R. Hunt, “A stretched exponential bound on the rate of growth of the number of periodic points for prevalent diffeomorphisms II,” <i>Electronic Research Announcements of the American Mathematical Society</i>, vol. 7, no. 5. American Mathematical Society, pp. 28–36, 2001.","apa":"Kaloshin, V., &#38; Hunt, B. R. (2001). A stretched exponential bound on the rate of growth of the number of periodic points for prevalent diffeomorphisms II. <i>Electronic Research Announcements of the American Mathematical Society</i>. American Mathematical Society. <a href=\"https://doi.org/10.1090/s1079-6762-01-00091-9\">https://doi.org/10.1090/s1079-6762-01-00091-9</a>","ama":"Kaloshin V, Hunt BR. A stretched exponential bound on the rate of growth of the number of periodic points for prevalent diffeomorphisms II. <i>Electronic Research Announcements of the American Mathematical Society</i>. 2001;7(5):28-36. doi:<a href=\"https://doi.org/10.1090/s1079-6762-01-00091-9\">10.1090/s1079-6762-01-00091-9</a>","chicago":"Kaloshin, Vadim, and Brian R. Hunt. “A Stretched Exponential Bound on the Rate of Growth of the Number of Periodic Points for Prevalent Diffeomorphisms II.” <i>Electronic Research Announcements of the American Mathematical Society</i>. American Mathematical Society, 2001. <a href=\"https://doi.org/10.1090/s1079-6762-01-00091-9\">https://doi.org/10.1090/s1079-6762-01-00091-9</a>.","ista":"Kaloshin V, Hunt BR. 2001. A stretched exponential bound on the rate of growth of the number of periodic points for prevalent diffeomorphisms II. Electronic Research Announcements of the American Mathematical Society. 7(5), 28–36.","short":"V. Kaloshin, B.R. Hunt, Electronic Research Announcements of the American Mathematical Society 7 (2001) 28–36."},"fulldoi":"https://doi.org/10.1090/s1079-6762-01-00091-9","day":"24","article_type":"original","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"None","month":"04","date_updated":"2021-01-12T08:19:51Z","doi":"10.1090/s1079-6762-01-00091-9","date_created":"2020-09-18T10:49:43Z","type":"journal_article","page":"28-36","keyword":["General Mathematics"],"quality_controlled":"1","issue":"5","article_processing_charge":"No","publisher":"American Mathematical Society","_id":"8521","publication":"Electronic Research Announcements of the American Mathematical Society","volume":7,"language":[{"iso":"eng"}],"intvolume":"         7","status":"public","abstract":[{"text":"We continue the previous article's discussion of bounds, for prevalent diffeomorphisms of smooth compact manifolds, on the growth of the number of periodic points and the decay of their hyperbolicity as a function of their period $n$. In that article we reduced the main results to a problem, for certain families of diffeomorphisms, of bounding the measure of parameter values for which the diffeomorphism has (for a given period $n$) an almost periodic point that is almost nonhyperbolic. We also formulated our results for $1$-dimensional endomorphisms on a compact interval. In this article we describe some of the main techniques involved and outline the rest of the proof. To simplify notation, we concentrate primarily on the $1$-dimensional case.","lang":"eng"}],"year":"2001","publication_status":"published","extern":"1","author":[{"orcid":"0000-0002-6051-2628","first_name":"Vadim","last_name":"Kaloshin","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","full_name":"Kaloshin, Vadim"},{"last_name":"Hunt","first_name":"Brian R.","full_name":"Hunt, Brian R."}],"title":"A stretched exponential bound on the rate of growth of the number of periodic points for prevalent diffeomorphisms II","date_published":"2001-04-24T00:00:00Z"},{"date_created":"2020-09-18T10:49:56Z","date_updated":"2021-01-12T08:19:51Z","doi":"10.1090/s1079-6762-01-00090-7","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"None","month":"04","page":"17-27","type":"journal_article","fulldoi":"https://doi.org/10.1090/s1079-6762-01-00090-7","publication_identifier":{"issn":["1079-6762"]},"citation":{"apa":"Kaloshin, V., &#38; Hunt, B. R. (2001). A stretched exponential bound on the rate of growth of the number of periodic points for prevalent diffeomorphisms I. <i>Electronic Research Announcements of the American Mathematical Society</i>. American Mathematical Society. <a href=\"https://doi.org/10.1090/s1079-6762-01-00090-7\">https://doi.org/10.1090/s1079-6762-01-00090-7</a>","ieee":"V. Kaloshin and B. R. Hunt, “A stretched exponential bound on the rate of growth of the number of periodic points for prevalent diffeomorphisms I,” <i>Electronic Research Announcements of the American Mathematical Society</i>, vol. 7, no. 4. American Mathematical Society, pp. 17–27, 2001.","mla":"Kaloshin, Vadim, and Brian R. Hunt. “A Stretched Exponential Bound on the Rate of Growth of the Number of Periodic Points for Prevalent Diffeomorphisms I.” <i>Electronic Research Announcements of the American Mathematical Society</i>, vol. 7, no. 4, American Mathematical Society, 2001, pp. 17–27, doi:<a href=\"https://doi.org/10.1090/s1079-6762-01-00090-7\">10.1090/s1079-6762-01-00090-7</a>.","ama":"Kaloshin V, Hunt BR. A stretched exponential bound on the rate of growth of the number of periodic points for prevalent diffeomorphisms I. <i>Electronic Research Announcements of the American Mathematical Society</i>. 2001;7(4):17-27. doi:<a href=\"https://doi.org/10.1090/s1079-6762-01-00090-7\">10.1090/s1079-6762-01-00090-7</a>","short":"V. Kaloshin, B.R. Hunt, Electronic Research Announcements of the American Mathematical Society 7 (2001) 17–27.","chicago":"Kaloshin, Vadim, and Brian R. Hunt. “A Stretched Exponential Bound on the Rate of Growth of the Number of Periodic Points for Prevalent Diffeomorphisms I.” <i>Electronic Research Announcements of the American Mathematical Society</i>. American Mathematical Society, 2001. <a href=\"https://doi.org/10.1090/s1079-6762-01-00090-7\">https://doi.org/10.1090/s1079-6762-01-00090-7</a>.","ista":"Kaloshin V, Hunt BR. 2001. A stretched exponential bound on the rate of growth of the number of periodic points for prevalent diffeomorphisms I. Electronic Research Announcements of the American Mathematical Society. 7(4), 17–27."},"day":"18","article_type":"original","year":"2001","publication_status":"published","extern":"1","date_published":"2001-04-18T00:00:00Z","title":"A stretched exponential bound on the rate of growth of the number of periodic points for prevalent diffeomorphisms I","author":[{"last_name":"Kaloshin","first_name":"Vadim","orcid":"0000-0002-6051-2628","full_name":"Kaloshin, Vadim","id":"FE553552-CDE8-11E9-B324-C0EBE5697425"},{"full_name":"Hunt, Brian R.","first_name":"Brian R.","last_name":"Hunt"}],"article_processing_charge":"No","publisher":"American Mathematical Society","_id":"8522","keyword":["General Mathematics"],"quality_controlled":"1","issue":"4","language":[{"iso":"eng"}],"status":"public","intvolume":"         7","abstract":[{"text":"For diffeomorphisms of smooth compact manifolds, we consider the problem of how fast the number of periodic points with period $n$grows as a function of $n$. In many familiar cases (e.g., Anosov systems) the growth is exponential, but arbitrarily fast growth is possible; in fact, the first author has shown that arbitrarily fast growth is topologically (Baire) generic for $C^2$ or smoother diffeomorphisms. In the present work we show that, by contrast, for a measure-theoretic notion of genericity we call ``prevalence'', the growth is not much faster than exponential. Specifically, we show that for each $\\delta > 0$, there is a prevalent set of ( $C^{1+\\rho}$ or smoother) diffeomorphisms for which the number of period $n$ points is bounded above by $\\operatorname{exp}(C n^{1+\\delta})$ for some $C$ independent of $n$. We also obtain a related bound on the decay of the hyperbolicity of the periodic points as a function of $n$. The contrast between topologically generic and measure-theoretically generic behavior for the growth of the number of periodic points and the decay of their hyperbolicity shows this to be a subtle and complex phenomenon, reminiscent of KAM theory.","lang":"eng"}],"publication":"Electronic Research Announcements of the American Mathematical Society","volume":7},{"publication":"Journal of Algorithms","volume":34,"language":[{"iso":"eng"}],"status":"public","intvolume":"        34","abstract":[{"text":"The vertex connectivity κ of a graph is the smallest number of vertices whose deletion separates the graph or makes it trivial. We present the fastest known deterministic algorithm for finding the vertex connectivity and a corresponding separator. The time for a digraph having n vertices and m edges is O(min{κ3 + n, κn}m); for an undirected graph the term m can be replaced by κn. A randomized algorithm finds κ with error probability 1/2 in time O(nm). If the vertices have nonnegative weights the weighted vertex connectivity is found in time O(κ1nmlog(n2/m)) where κ1 ≤ m/n is the unweighted vertex connectivity or in expected time O(nmlog(n2/m)) with error probability 1/2. The main algorithm combines two previous vertex connectivity algorithms and a generalization of the preflow-push algorithm of Hao and Orlin (1994, J. Algorithms17, 424–446) that computes edge connectivity.","lang":"eng"}],"issue":"2","quality_controlled":"1","keyword":["Computational Theory and Mathematics","Computational Mathematics","Control and Optimization"],"_id":"11683","article_processing_charge":"No","publisher":"Elsevier","title":"Computing vertex connectivity: New bounds from old techniques","author":[{"full_name":"Henzinger, Monika H","id":"540c9bbd-f2de-11ec-812d-d04a5be85630","last_name":"Henzinger","orcid":"0000-0002-5008-6530","first_name":"Monika H"},{"last_name":"Rao","first_name":"Satish","full_name":"Rao, Satish"},{"last_name":"Gabow","first_name":"Harold N.","full_name":"Gabow, Harold N."}],"date_published":"2000-02-01T00:00:00Z","extern":"1","publication_status":"published","year":"2000","article_type":"original","day":"01","fulldoi":"https://doi.org/10.1006/jagm.1999.1055","publication_identifier":{"issn":["0196-6774"]},"citation":{"mla":"Henzinger, Monika, et al. “Computing Vertex Connectivity: New Bounds from Old Techniques.” <i>Journal of Algorithms</i>, vol. 34, no. 2, Elsevier, 2000, pp. 222–50, doi:<a href=\"https://doi.org/10.1006/jagm.1999.1055\">10.1006/jagm.1999.1055</a>.","ieee":"M. Henzinger, S. Rao, and H. N. Gabow, “Computing vertex connectivity: New bounds from old techniques,” <i>Journal of Algorithms</i>, vol. 34, no. 2. Elsevier, pp. 222–250, 2000.","apa":"Henzinger, M., Rao, S., &#38; Gabow, H. N. (2000). Computing vertex connectivity: New bounds from old techniques. <i>Journal of Algorithms</i>. Elsevier. <a href=\"https://doi.org/10.1006/jagm.1999.1055\">https://doi.org/10.1006/jagm.1999.1055</a>","ama":"Henzinger M, Rao S, Gabow HN. Computing vertex connectivity: New bounds from old techniques. <i>Journal of Algorithms</i>. 2000;34(2):222-250. doi:<a href=\"https://doi.org/10.1006/jagm.1999.1055\">10.1006/jagm.1999.1055</a>","chicago":"Henzinger, Monika, Satish Rao, and Harold N. Gabow. “Computing Vertex Connectivity: New Bounds from Old Techniques.” <i>Journal of Algorithms</i>. Elsevier, 2000. <a href=\"https://doi.org/10.1006/jagm.1999.1055\">https://doi.org/10.1006/jagm.1999.1055</a>.","ista":"Henzinger M, Rao S, Gabow HN. 2000. Computing vertex connectivity: New bounds from old techniques. Journal of Algorithms. 34(2), 222–250.","short":"M. Henzinger, S. Rao, H.N. Gabow, Journal of Algorithms 34 (2000) 222–250."},"scopus_import":"1","type":"journal_article","page":"222-250","month":"02","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"None","doi":"10.1006/jagm.1999.1055","date_created":"2022-07-28T08:56:10Z","date_updated":"2024-11-04T11:42:08Z"},{"date_published":"1997-06-19T00:00:00Z","author":[{"last_name":"Hunt","first_name":"Brian R","full_name":"Hunt, Brian R"},{"first_name":"Vadim","orcid":"0000-0002-6051-2628","last_name":"Kaloshin","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","full_name":"Kaloshin, Vadim"}],"title":"How projections affect the dimension spectrum of fractal measures","year":"1997","publication_status":"published","extern":"1","status":"public","language":[{"iso":"eng"}],"intvolume":"        10","abstract":[{"text":"We introduce a new potential-theoretic definition of the dimension spectrum  of a probability measure for q > 1 and explain its relation to prior definitions. We apply this definition to prove that if  and  is a Borel probability measure with compact support in , then under almost every linear transformation from  to , the q-dimension of the image of  is ; in particular, the q-dimension of  is preserved provided . We also present results on the preservation of information dimension  and pointwise dimension. Finally, for  and q > 2 we give examples for which  is not preserved by any linear transformation into . All results for typical linear transformations are also proved for typical (in the sense of prevalence) continuously differentiable functions.","lang":"eng"}],"publication":"Nonlinearity","volume":10,"publisher":"IOP Publishing","article_processing_charge":"No","_id":"8527","quality_controlled":"1","keyword":["Mathematical Physics","General Physics and Astronomy","Applied Mathematics","Statistical and Nonlinear Physics"],"issue":"5","page":"1031-1046","type":"journal_article","doi":"10.1088/0951-7715/10/5/002","date_updated":"2021-01-12T08:19:53Z","date_created":"2020-09-18T10:50:41Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"None","month":"06","day":"19","article_type":"original","publication_identifier":{"issn":["0951-7715","1361-6544"]},"citation":{"ama":"Hunt BR, Kaloshin V. How projections affect the dimension spectrum of fractal measures. <i>Nonlinearity</i>. 1997;10(5):1031-1046. doi:<a href=\"https://doi.org/10.1088/0951-7715/10/5/002\">10.1088/0951-7715/10/5/002</a>","ieee":"B. R. Hunt and V. Kaloshin, “How projections affect the dimension spectrum of fractal measures,” <i>Nonlinearity</i>, vol. 10, no. 5. IOP Publishing, pp. 1031–1046, 1997.","apa":"Hunt, B. R., &#38; Kaloshin, V. (1997). How projections affect the dimension spectrum of fractal measures. <i>Nonlinearity</i>. IOP Publishing. <a href=\"https://doi.org/10.1088/0951-7715/10/5/002\">https://doi.org/10.1088/0951-7715/10/5/002</a>","mla":"Hunt, Brian R., and Vadim Kaloshin. “How Projections Affect the Dimension Spectrum of Fractal Measures.” <i>Nonlinearity</i>, vol. 10, no. 5, IOP Publishing, 1997, pp. 1031–46, doi:<a href=\"https://doi.org/10.1088/0951-7715/10/5/002\">10.1088/0951-7715/10/5/002</a>.","ista":"Hunt BR, Kaloshin V. 1997. How projections affect the dimension spectrum of fractal measures. Nonlinearity. 10(5), 1031–1046.","chicago":"Hunt, Brian R, and Vadim Kaloshin. “How Projections Affect the Dimension Spectrum of Fractal Measures.” <i>Nonlinearity</i>. IOP Publishing, 1997. <a href=\"https://doi.org/10.1088/0951-7715/10/5/002\">https://doi.org/10.1088/0951-7715/10/5/002</a>.","short":"B.R. Hunt, V. Kaloshin, Nonlinearity 10 (1997) 1031–1046."},"fulldoi":"https://doi.org/10.1088/0951-7715/10/5/002"}]