---
_id: '8419'
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’."
article_number: '20170419'
article_processing_charge: No
article_type: original
author:
- first_name: Vadim
full_name: Kaloshin, Vadim
id: FE553552-CDE8-11E9-B324-C0EBE5697425
last_name: Kaloshin
orcid: 0000-0002-6051-2628
- first_name: Alfonso
full_name: Sorrentino, Alfonso
last_name: Sorrentino
citation:
ama: 'Kaloshin V, Sorrentino A. On the integrability of Birkhoff billiards. Philosophical
Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.
2018;376(2131). doi:10.1098/rsta.2017.0419'
apa: 'Kaloshin, V., & Sorrentino, A. (2018). On the integrability of Birkhoff
billiards. Philosophical Transactions of the Royal Society A: Mathematical,
Physical and Engineering Sciences. The Royal Society. https://doi.org/10.1098/rsta.2017.0419'
chicago: 'Kaloshin, Vadim, and Alfonso Sorrentino. “On the Integrability of Birkhoff
Billiards.” Philosophical Transactions of the Royal Society A: Mathematical,
Physical and Engineering Sciences. The Royal Society, 2018. https://doi.org/10.1098/rsta.2017.0419.'
ieee: 'V. Kaloshin and A. Sorrentino, “On the integrability of Birkhoff billiards,”
Philosophical Transactions of the Royal Society A: Mathematical, Physical and
Engineering Sciences, vol. 376, no. 2131. The Royal Society, 2018.'
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.'
mla: 'Kaloshin, Vadim, and Alfonso Sorrentino. “On the Integrability of Birkhoff
Billiards.” Philosophical Transactions of the Royal Society A: Mathematical,
Physical and Engineering Sciences, vol. 376, no. 2131, 20170419, The Royal
Society, 2018, doi:10.1098/rsta.2017.0419.'
short: 'V. Kaloshin, A. Sorrentino, Philosophical Transactions of the Royal Society
A: Mathematical, Physical and Engineering Sciences 376 (2018).'
date_created: 2020-09-17T10:42:01Z
date_published: 2018-10-28T00:00:00Z
date_updated: 2021-01-12T08:19:09Z
day: '28'
doi: 10.1098/rsta.2017.0419
extern: '1'
fulldoi: https://doi.org/10.1098/rsta.2017.0419
intvolume: ' 376'
issue: '2131'
keyword:
- General Engineering
- General Physics and Astronomy
- General Mathematics
language:
- iso: eng
month: '10'
oa_version: None
publication: 'Philosophical Transactions of the Royal Society A: Mathematical, Physical
and Engineering Sciences'
publication_identifier:
issn:
- 1364-503X
- 1471-2962
publication_status: published
publisher: The Royal Society
quality_controlled: '1'
status: public
title: On the integrability of Birkhoff billiards
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 376
year: '2018'
...
---
_id: '8420'
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.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Vadim
full_name: Kaloshin, Vadim
id: FE553552-CDE8-11E9-B324-C0EBE5697425
last_name: Kaloshin
orcid: 0000-0002-6051-2628
- first_name: Ke
full_name: Zhang, Ke
last_name: Zhang
citation:
ama: Kaloshin V, Zhang K. Density of convex billiards with rational caustics. Nonlinearity.
2018;31(11):5214-5234. doi:10.1088/1361-6544/aadc12
apa: Kaloshin, V., & Zhang, K. (2018). Density of convex billiards with rational
caustics. Nonlinearity. IOP Publishing. https://doi.org/10.1088/1361-6544/aadc12
chicago: Kaloshin, Vadim, and Ke Zhang. “Density of Convex Billiards with Rational
Caustics.” Nonlinearity. IOP Publishing, 2018. https://doi.org/10.1088/1361-6544/aadc12.
ieee: V. Kaloshin and K. Zhang, “Density of convex billiards with rational caustics,”
Nonlinearity, vol. 31, no. 11. IOP Publishing, pp. 5214–5234, 2018.
ista: Kaloshin V, Zhang K. 2018. Density of convex billiards with rational caustics.
Nonlinearity. 31(11), 5214–5234.
mla: Kaloshin, Vadim, and Ke Zhang. “Density of Convex Billiards with Rational Caustics.”
Nonlinearity, vol. 31, no. 11, IOP Publishing, 2018, pp. 5214–34, doi:10.1088/1361-6544/aadc12.
short: V. Kaloshin, K. Zhang, Nonlinearity 31 (2018) 5214–5234.
date_created: 2020-09-17T10:42:09Z
date_published: 2018-10-15T00:00:00Z
date_updated: 2021-01-12T08:19:10Z
day: '15'
doi: 10.1088/1361-6544/aadc12
extern: '1'
external_id:
arxiv:
- '1706.07968'
fulldoi: https://doi.org/10.1088/1361-6544/aadc12
intvolume: ' 31'
issue: '11'
keyword:
- Mathematical Physics
- General Physics and Astronomy
- Applied Mathematics
- Statistical and Nonlinear Physics
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1706.07968
month: '10'
oa: 1
oa_version: Preprint
page: 5214-5234
publication: Nonlinearity
publication_identifier:
issn:
- 0951-7715
- 1361-6544
publication_status: published
publisher: IOP Publishing
quality_controlled: '1'
status: public
title: Density of convex billiards with rational caustics
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 31
year: '2018'
...
---
_id: '11670'
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.
acknowledgement: We would like to thank Veronika Loitzenbauer and the anonymous referees
for their valuable feedback.
article_number: '1'
article_processing_charge: No
article_type: original
author:
- first_name: Paul
full_name: Dütting, Paul
last_name: Dütting
- first_name: Monika H
full_name: Henzinger, Monika H
id: 540c9bbd-f2de-11ec-812d-d04a5be85630
last_name: Henzinger
orcid: 0000-0002-5008-6530
- first_name: Ingmar
full_name: Weber, Ingmar
last_name: Weber
citation:
ama: Dütting P, Henzinger M, Weber I. An expressive mechanism for auctions on the
web. ACM Transactions on Economics and Computation. 2015;4(1). doi:10.1145/2716312
apa: Dütting, P., Henzinger, M., & Weber, I. (2015). An expressive mechanism
for auctions on the web. ACM Transactions on Economics and Computation.
Association for Computing Machinery. https://doi.org/10.1145/2716312
chicago: Dütting, Paul, Monika Henzinger, and Ingmar Weber. “An Expressive Mechanism
for Auctions on the Web.” ACM Transactions on Economics and Computation.
Association for Computing Machinery, 2015. https://doi.org/10.1145/2716312.
ieee: P. Dütting, M. Henzinger, and I. Weber, “An expressive mechanism for auctions
on the web,” ACM Transactions on Economics and Computation, vol. 4, no.
1. Association for Computing Machinery, 2015.
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.
mla: Dütting, Paul, et al. “An Expressive Mechanism for Auctions on the Web.” ACM
Transactions on Economics and Computation, vol. 4, no. 1, 1, Association for
Computing Machinery, 2015, doi:10.1145/2716312.
short: P. Dütting, M. Henzinger, I. Weber, ACM Transactions on Economics and Computation
4 (2015).
date_created: 2022-07-27T12:43:18Z
date_published: 2015-12-02T00:00:00Z
date_updated: 2024-11-06T12:07:05Z
day: '02'
doi: 10.1145/2716312
extern: '1'
fulldoi: https://doi.org/10.1145/2716312
intvolume: ' 4'
issue: '1'
keyword:
- Computational Mathematics
- Marketing
- Economics and Econometrics
- Statistics and Probability
- Computer Science (miscellaneous)
language:
- iso: eng
month: '12'
oa_version: None
publication: ACM Transactions on Economics and Computation
publication_identifier:
eissn:
- 2167-8383
issn:
- 2167-8375
publication_status: published
publisher: Association for Computing Machinery
quality_controlled: '1'
scopus_import: '1'
status: public
title: An expressive mechanism for auctions on the web
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 4
year: '2015'
...
---
_id: '8498'
abstract:
- lang: eng
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]."
article_processing_charge: No
article_type: original
author:
- first_name: Vadim
full_name: Kaloshin, Vadim
id: FE553552-CDE8-11E9-B324-C0EBE5697425
last_name: Kaloshin
orcid: 0000-0002-6051-2628
- first_name: K
full_name: Zhang, K
last_name: Zhang
citation:
ama: Kaloshin V, Zhang K. Arnold diffusion for smooth convex systems of two and
a half degrees of freedom. Nonlinearity. 2015;28(8):2699-2720. doi:10.1088/0951-7715/28/8/2699
apa: Kaloshin, V., & Zhang, K. (2015). Arnold diffusion for smooth convex systems
of two and a half degrees of freedom. Nonlinearity. IOP Publishing. https://doi.org/10.1088/0951-7715/28/8/2699
chicago: Kaloshin, Vadim, and K Zhang. “Arnold Diffusion for Smooth Convex Systems
of Two and a Half Degrees of Freedom.” Nonlinearity. IOP Publishing, 2015.
https://doi.org/10.1088/0951-7715/28/8/2699.
ieee: V. Kaloshin and K. Zhang, “Arnold diffusion for smooth convex systems of two
and a half degrees of freedom,” Nonlinearity, vol. 28, no. 8. IOP Publishing,
pp. 2699–2720, 2015.
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.
mla: Kaloshin, Vadim, and K. Zhang. “Arnold Diffusion for Smooth Convex Systems
of Two and a Half Degrees of Freedom.” Nonlinearity, vol. 28, no. 8, IOP
Publishing, 2015, pp. 2699–720, doi:10.1088/0951-7715/28/8/2699.
short: V. Kaloshin, K. Zhang, Nonlinearity 28 (2015) 2699–2720.
date_created: 2020-09-18T10:46:43Z
date_published: 2015-06-30T00:00:00Z
date_updated: 2021-01-12T08:19:41Z
day: '30'
doi: 10.1088/0951-7715/28/8/2699
extern: '1'
fulldoi: https://doi.org/10.1088/0951-7715/28/8/2699
intvolume: ' 28'
issue: '8'
keyword:
- Mathematical Physics
- General Physics and Astronomy
- Applied Mathematics
- Statistical and Nonlinear Physics
language:
- iso: eng
month: '06'
oa_version: None
page: 2699-2720
publication: Nonlinearity
publication_identifier:
issn:
- 0951-7715
- 1361-6544
publication_status: published
publisher: IOP Publishing
quality_controlled: '1'
status: public
title: Arnold diffusion for smooth convex systems of two and a half degrees of freedom
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 28
year: '2015'
...
---
_id: '8459'
abstract:
- lang: eng
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.
article_processing_charge: No
article_type: original
author:
- first_name: Sébastien
full_name: Morin, Sébastien
last_name: Morin
- first_name: Troels E
full_name: Linnet, Troels E
last_name: Linnet
- first_name: Mathilde
full_name: Lescanne, Mathilde
last_name: Lescanne
- first_name: Paul
full_name: Schanda, Paul
id: 7B541462-FAF6-11E9-A490-E8DFE5697425
last_name: Schanda
orcid: 0000-0002-9350-7606
- first_name: Gary S
full_name: Thompson, Gary S
last_name: Thompson
- first_name: Martin
full_name: Tollinger, Martin
last_name: Tollinger
- first_name: Kaare
full_name: Teilum, Kaare
last_name: Teilum
- first_name: Stéphane
full_name: Gagné, Stéphane
last_name: Gagné
- first_name: Dominique
full_name: Marion, Dominique
last_name: Marion
- first_name: Christian
full_name: Griesinger, Christian
last_name: Griesinger
- first_name: Martin
full_name: Blackledge, Martin
last_name: Blackledge
- first_name: Edward J
full_name: d’Auvergne, Edward J
last_name: d’Auvergne
citation:
ama: 'Morin S, Linnet TE, Lescanne M, et al. Relax: The analysis of biomolecular
kinetics and thermodynamics using NMR relaxation dispersion data. Bioinformatics.
2014;30(15):2219-2220. doi:10.1093/bioinformatics/btu166'
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. Bioinformatics. Oxford
University Press. https://doi.org/10.1093/bioinformatics/btu166'
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.” Bioinformatics.
Oxford University Press, 2014. https://doi.org/10.1093/bioinformatics/btu166.'
ieee: 'S. Morin et al., “Relax: The analysis of biomolecular kinetics and
thermodynamics using NMR relaxation dispersion data,” Bioinformatics, vol.
30, no. 15. Oxford University Press, pp. 2219–2220, 2014.'
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.'
mla: 'Morin, Sébastien, et al. “Relax: The Analysis of Biomolecular Kinetics and
Thermodynamics Using NMR Relaxation Dispersion Data.” Bioinformatics, vol.
30, no. 15, Oxford University Press, 2014, pp. 2219–20, doi:10.1093/bioinformatics/btu166.'
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.
date_created: 2020-09-18T10:08:07Z
date_published: 2014-08-01T00:00:00Z
date_updated: 2021-01-12T08:19:25Z
day: '01'
doi: 10.1093/bioinformatics/btu166
extern: '1'
fulldoi: https://doi.org/10.1093/bioinformatics/btu166
intvolume: ' 30'
issue: '15'
keyword:
- Statistics and Probability
- Computational Theory and Mathematics
- Biochemistry
- Molecular Biology
- Computational Mathematics
- Computer Science Applications
language:
- iso: eng
month: '08'
oa_version: None
page: 2219-2220
publication: Bioinformatics
publication_identifier:
issn:
- 1367-4803
- 1460-2059
publication_status: published
publisher: Oxford University Press
quality_controlled: '1'
related_material:
link:
- relation: erratum
url: https://doi.org/10.1093/bioinformatics/btz397
status: public
title: 'Relax: The analysis of biomolecular kinetics and thermodynamics using NMR
relaxation dispersion data'
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 30
year: '2014'
...
---
_id: '8500'
abstract:
- lang: eng
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.
article_processing_charge: No
article_type: original
author:
- first_name: Vadim
full_name: Kaloshin, Vadim
id: FE553552-CDE8-11E9-B324-C0EBE5697425
last_name: Kaloshin
orcid: 0000-0002-6051-2628
- first_name: Mark
full_name: Levi, Mark
last_name: Levi
- first_name: Maria
full_name: Saprykina, Maria
last_name: Saprykina
citation:
ama: Kaloshin V, Levi M, Saprykina M. Arnol′d diffusion in a pendulum lattice. Communications
on Pure and Applied Mathematics. 2014;67(5):748-775. doi:10.1002/cpa.21509
apa: Kaloshin, V., Levi, M., & Saprykina, M. (2014). Arnol′d diffusion in a
pendulum lattice. Communications on Pure and Applied Mathematics. Wiley.
https://doi.org/10.1002/cpa.21509
chicago: Kaloshin, Vadim, Mark Levi, and Maria Saprykina. “Arnol′d Diffusion in
a Pendulum Lattice.” Communications on Pure and Applied Mathematics. Wiley,
2014. https://doi.org/10.1002/cpa.21509.
ieee: V. Kaloshin, M. Levi, and M. Saprykina, “Arnol′d diffusion in a pendulum lattice,”
Communications on Pure and Applied Mathematics, vol. 67, no. 5. Wiley,
pp. 748–775, 2014.
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.
mla: Kaloshin, Vadim, et al. “Arnol′d Diffusion in a Pendulum Lattice.” Communications
on Pure and Applied Mathematics, vol. 67, no. 5, Wiley, 2014, pp. 748–75,
doi:10.1002/cpa.21509.
short: V. Kaloshin, M. Levi, M. Saprykina, Communications on Pure and Applied Mathematics
67 (2014) 748–775.
date_created: 2020-09-18T10:47:01Z
date_published: 2014-05-01T00:00:00Z
date_updated: 2022-08-25T13:58:13Z
day: '01'
doi: 10.1002/cpa.21509
extern: '1'
fulldoi: https://doi.org/10.1002/cpa.21509
intvolume: ' 67'
issue: '5'
keyword:
- Applied Mathematics
- General Mathematics
language:
- iso: eng
month: '05'
oa_version: None
page: 748-775
publication: Communications on Pure and Applied Mathematics
publication_identifier:
issn:
- 0010-3640
publication_status: published
publisher: Wiley
quality_controlled: '1'
status: public
title: Arnol′d diffusion in a pendulum lattice
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 67
year: '2014'
...
---
_id: '8501'
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.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Abed
full_name: Bounemoura, Abed
last_name: Bounemoura
- first_name: Vadim
full_name: Kaloshin, Vadim
id: FE553552-CDE8-11E9-B324-C0EBE5697425
last_name: Kaloshin
orcid: 0000-0002-6051-2628
citation:
ama: Bounemoura A, Kaloshin V. Generic fast diffusion for a class of non-convex
Hamiltonians with two degrees of freedom. Moscow Mathematical Journal.
2014;14(2):181-203. doi:10.17323/1609-4514-2014-14-2-181-203
apa: Bounemoura, A., & Kaloshin, V. (2014). Generic fast diffusion for a class
of non-convex Hamiltonians with two degrees of freedom. Moscow Mathematical
Journal. Independent University of Moscow. https://doi.org/10.17323/1609-4514-2014-14-2-181-203
chicago: Bounemoura, Abed, and Vadim Kaloshin. “Generic Fast Diffusion for a Class
of Non-Convex Hamiltonians with Two Degrees of Freedom.” Moscow Mathematical
Journal. Independent University of Moscow, 2014. https://doi.org/10.17323/1609-4514-2014-14-2-181-203.
ieee: A. Bounemoura and V. Kaloshin, “Generic fast diffusion for a class of non-convex
Hamiltonians with two degrees of freedom,” Moscow Mathematical Journal,
vol. 14, no. 2. Independent University of Moscow, pp. 181–203, 2014.
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.
mla: Bounemoura, Abed, and Vadim Kaloshin. “Generic Fast Diffusion for a Class of
Non-Convex Hamiltonians with Two Degrees of Freedom.” Moscow Mathematical Journal,
vol. 14, no. 2, Independent University of Moscow, 2014, pp. 181–203, doi:10.17323/1609-4514-2014-14-2-181-203.
short: A. Bounemoura, V. Kaloshin, Moscow Mathematical Journal 14 (2014) 181–203.
date_created: 2020-09-18T10:47:09Z
date_published: 2014-04-01T00:00:00Z
date_updated: 2021-01-12T08:19:43Z
day: '01'
doi: 10.17323/1609-4514-2014-14-2-181-203
extern: '1'
external_id:
arxiv:
- '1304.3050'
fulldoi: https://doi.org/10.17323/1609-4514-2014-14-2-181-203
intvolume: ' 14'
issue: '2'
keyword:
- General Mathematics
language:
- iso: eng
month: '04'
oa_version: Preprint
page: 181-203
publication: Moscow Mathematical Journal
publication_identifier:
issn:
- 1609-3321
- 1609-4514
publication_status: published
publisher: Independent University of Moscow
quality_controlled: '1'
status: public
title: Generic fast diffusion for a class of non-convex Hamiltonians with two degrees
of freedom
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 14
year: '2014'
...
---
_id: '9166'
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.
article_number: '20130372'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Jérémie A
full_name: Palacci, Jérémie A
id: 8fb92548-2b22-11eb-b7c1-a3f0d08d7c7d
last_name: Palacci
orcid: 0000-0002-7253-9465
- first_name: S.
full_name: Sacanna, S.
last_name: Sacanna
- first_name: S.-H.
full_name: Kim, S.-H.
last_name: Kim
- first_name: G.-R.
full_name: Yi, G.-R.
last_name: Yi
- first_name: D. J.
full_name: Pine, D. J.
last_name: Pine
- first_name: P. M.
full_name: Chaikin, P. M.
last_name: Chaikin
citation:
ama: 'Palacci JA, Sacanna S, Kim S-H, Yi G-R, Pine DJ, Chaikin PM. Light-activated
self-propelled colloids. Philosophical Transactions of the Royal Society A:
Mathematical, Physical and Engineering Sciences. 2014;372(2029). doi:10.1098/rsta.2013.0372'
apa: 'Palacci, J. A., Sacanna, S., Kim, S.-H., Yi, G.-R., Pine, D. J., & Chaikin,
P. M. (2014). Light-activated self-propelled colloids. Philosophical Transactions
of the Royal Society A: Mathematical, Physical and Engineering Sciences. The
Royal Society. https://doi.org/10.1098/rsta.2013.0372'
chicago: 'Palacci, Jérémie A, S. Sacanna, S.-H. Kim, G.-R. Yi, D. J. Pine, and P.
M. Chaikin. “Light-Activated Self-Propelled Colloids.” Philosophical Transactions
of the Royal Society A: Mathematical, Physical and Engineering Sciences. The
Royal Society, 2014. https://doi.org/10.1098/rsta.2013.0372.'
ieee: 'J. A. Palacci, S. Sacanna, S.-H. Kim, G.-R. Yi, D. J. Pine, and P. M. Chaikin,
“Light-activated self-propelled colloids,” Philosophical Transactions of the
Royal Society A: Mathematical, Physical and Engineering Sciences, vol. 372,
no. 2029. The Royal Society, 2014.'
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.'
mla: 'Palacci, Jérémie A., et al. “Light-Activated Self-Propelled Colloids.” Philosophical
Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences,
vol. 372, no. 2029, 20130372, The Royal Society, 2014, doi:10.1098/rsta.2013.0372.'
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).'
date_created: 2021-02-18T14:31:11Z
date_published: 2014-11-28T00:00:00Z
date_updated: 2021-02-22T10:44:16Z
day: '28'
doi: 10.1098/rsta.2013.0372
extern: '1'
external_id:
arxiv:
- '1410.7278'
pmid:
- '25332383'
fulldoi: https://doi.org/10.1098/rsta.2013.0372
intvolume: ' 372'
issue: '2029'
keyword:
- General Engineering
- General Physics and Astronomy
- General Mathematics
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.1098/rsta.2013.0372
month: '11'
oa: 1
oa_version: Published Version
pmid: 1
publication: 'Philosophical Transactions of the Royal Society A: Mathematical, Physical
and Engineering Sciences'
publication_identifier:
eissn:
- 1471-2962
issn:
- 1364-503X
publication_status: published
publisher: The Royal Society
quality_controlled: '1'
scopus_import: '1'
status: public
title: Light-activated self-propelled colloids
type: journal_article
user_id: D865714E-FA4E-11E9-B85B-F5C5E5697425
volume: 372
year: '2014'
...
---
_id: '8504'
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.
article_processing_charge: No
article_type: original
author:
- first_name: Vadim
full_name: Kaloshin, Vadim
id: FE553552-CDE8-11E9-B324-C0EBE5697425
last_name: Kaloshin
orcid: 0000-0002-6051-2628
- first_name: O. S.
full_name: KOZLOVSKI, O. S.
last_name: KOZLOVSKI
citation:
ama: Kaloshin V, KOZLOVSKI OS. A Cr unimodal map with an arbitrary fast growth of
the number of periodic points. Ergodic Theory and Dynamical Systems. 2012;32(1):159-165.
doi:10.1017/s0143385710000817
apa: Kaloshin, V., & KOZLOVSKI, O. S. (2012). A Cr unimodal map with an arbitrary
fast growth of the number of periodic points. Ergodic Theory and Dynamical
Systems. Cambridge University Press. https://doi.org/10.1017/s0143385710000817
chicago: Kaloshin, Vadim, and O. S. KOZLOVSKI. “A Cr Unimodal Map with an Arbitrary
Fast Growth of the Number of Periodic Points.” Ergodic Theory and Dynamical
Systems. Cambridge University Press, 2012. https://doi.org/10.1017/s0143385710000817.
ieee: V. Kaloshin and O. S. KOZLOVSKI, “A Cr unimodal map with an arbitrary fast
growth of the number of periodic points,” Ergodic Theory and Dynamical Systems,
vol. 32, no. 1. Cambridge University Press, pp. 159–165, 2012.
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.
mla: Kaloshin, Vadim, and O. S. KOZLOVSKI. “A Cr Unimodal Map with an Arbitrary
Fast Growth of the Number of Periodic Points.” Ergodic Theory and Dynamical
Systems, vol. 32, no. 1, Cambridge University Press, 2012, pp. 159–65, doi:10.1017/s0143385710000817.
short: V. Kaloshin, O.S. KOZLOVSKI, Ergodic Theory and Dynamical Systems 32 (2012)
159–165.
date_created: 2020-09-18T10:47:33Z
date_published: 2012-02-01T00:00:00Z
date_updated: 2021-01-12T08:19:44Z
day: '01'
doi: 10.1017/s0143385710000817
extern: '1'
fulldoi: https://doi.org/10.1017/s0143385710000817
intvolume: ' 32'
issue: '1'
keyword:
- Applied Mathematics
- General Mathematics
language:
- iso: eng
month: '02'
oa_version: None
page: 159-165
publication: Ergodic Theory and Dynamical Systems
publication_identifier:
issn:
- 0143-3857
- 1469-4417
publication_status: published
publisher: Cambridge University Press
quality_controlled: '1'
status: public
title: A Cr unimodal map with an arbitrary fast growth of the number of periodic points
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 32
year: '2012'
...
---
_id: '8505'
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.
article_processing_charge: No
article_type: original
author:
- first_name: Joseph
full_name: Galante, Joseph
last_name: Galante
- first_name: Vadim
full_name: Kaloshin, Vadim
id: FE553552-CDE8-11E9-B324-C0EBE5697425
last_name: Kaloshin
orcid: 0000-0002-6051-2628
citation:
ama: Galante J, Kaloshin V. Destruction of invariant curves in the restricted circular
planar three-body problem by using comparison of action. Duke Mathematical
Journal. 2011;159(2):275-327. doi:10.1215/00127094-1415878
apa: 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. Duke University Press. https://doi.org/10.1215/00127094-1415878
chicago: Galante, Joseph, and Vadim Kaloshin. “Destruction of Invariant Curves in
the Restricted Circular Planar Three-Body Problem by Using Comparison of Action.”
Duke Mathematical Journal. Duke University Press, 2011. https://doi.org/10.1215/00127094-1415878.
ieee: J. Galante and V. Kaloshin, “Destruction of invariant curves in the restricted
circular planar three-body problem by using comparison of action,” Duke Mathematical
Journal, vol. 159, no. 2. Duke University Press, pp. 275–327, 2011.
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.
mla: Galante, Joseph, and Vadim Kaloshin. “Destruction of Invariant Curves in the
Restricted Circular Planar Three-Body Problem by Using Comparison of Action.”
Duke Mathematical Journal, vol. 159, no. 2, Duke University Press, 2011,
pp. 275–327, doi:10.1215/00127094-1415878.
short: J. Galante, V. Kaloshin, Duke Mathematical Journal 159 (2011) 275–327.
date_created: 2020-09-18T10:47:41Z
date_published: 2011-08-04T00:00:00Z
date_updated: 2021-01-12T08:19:45Z
day: '04'
doi: 10.1215/00127094-1415878
extern: '1'
fulldoi: https://doi.org/10.1215/00127094-1415878
intvolume: ' 159'
issue: '2'
keyword:
- General Mathematics
language:
- iso: eng
month: '08'
oa_version: None
page: 275-327
publication: Duke Mathematical Journal
publication_identifier:
issn:
- 0012-7094
publication_status: published
publisher: Duke University Press
quality_controlled: '1'
status: public
title: Destruction of invariant curves in the restricted circular planar three-body
problem by using comparison of action
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 159
year: '2011'
...
---
_id: '8508'
abstract:
- lang: eng
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.
article_processing_charge: No
article_type: original
author:
- first_name: Anton
full_name: Gorodetski, Anton
last_name: Gorodetski
- first_name: Vadim
full_name: Kaloshin, Vadim
id: FE553552-CDE8-11E9-B324-C0EBE5697425
last_name: Kaloshin
orcid: 0000-0002-6051-2628
citation:
ama: Gorodetski A, Kaloshin V. Conservative homoclinic bifurcations and some applications.
Proceedings of the Steklov Institute of Mathematics. 2009;267(1):76-90.
doi:10.1134/s0081543809040063
apa: Gorodetski, A., & Kaloshin, V. (2009). Conservative homoclinic bifurcations
and some applications. Proceedings of the Steklov Institute of Mathematics.
Springer Nature. https://doi.org/10.1134/s0081543809040063
chicago: Gorodetski, Anton, and Vadim Kaloshin. “Conservative Homoclinic Bifurcations
and Some Applications.” Proceedings of the Steklov Institute of Mathematics.
Springer Nature, 2009. https://doi.org/10.1134/s0081543809040063.
ieee: A. Gorodetski and V. Kaloshin, “Conservative homoclinic bifurcations and some
applications,” Proceedings of the Steklov Institute of Mathematics, vol.
267, no. 1. Springer Nature, pp. 76–90, 2009.
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.” Proceedings of the Steklov Institute of Mathematics,
vol. 267, no. 1, Springer Nature, 2009, pp. 76–90, doi:10.1134/s0081543809040063.
short: A. Gorodetski, V. Kaloshin, Proceedings of the Steklov Institute of Mathematics
267 (2009) 76–90.
date_created: 2020-09-18T10:48:03Z
date_published: 2009-12-01T00:00:00Z
date_updated: 2021-01-12T08:19:46Z
day: '01'
doi: 10.1134/s0081543809040063
extern: '1'
fulldoi: https://doi.org/10.1134/s0081543809040063
intvolume: ' 267'
issue: '1'
keyword:
- Mathematics (miscellaneous)
language:
- iso: eng
month: '12'
oa_version: None
page: 76-90
publication: Proceedings of the Steklov Institute of Mathematics
publication_identifier:
issn:
- 0081-5438
- 1531-8605
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
status: public
title: Conservative homoclinic bifurcations and some applications
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 267
year: '2009'
...
---
_id: '8509'
abstract:
- lang: eng
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} $.
article_processing_charge: No
article_type: original
author:
- first_name: Vadim
full_name: Kaloshin, Vadim
id: FE553552-CDE8-11E9-B324-C0EBE5697425
last_name: Kaloshin
orcid: 0000-0002-6051-2628
- first_name: Mark
full_name: Levi, Mark
last_name: Levi
citation:
ama: Kaloshin V, Levi M. Geometry of Arnold diffusion. SIAM Review. 2008;50(4):702-720.
doi:10.1137/070703235
apa: Kaloshin, V., & Levi, M. (2008). Geometry of Arnold diffusion. SIAM
Review. Society for Industrial & Applied Mathematics. https://doi.org/10.1137/070703235
chicago: Kaloshin, Vadim, and Mark Levi. “Geometry of Arnold Diffusion.” SIAM
Review. Society for Industrial & Applied Mathematics, 2008. https://doi.org/10.1137/070703235.
ieee: V. Kaloshin and M. Levi, “Geometry of Arnold diffusion,” SIAM Review,
vol. 50, no. 4. Society for Industrial & Applied Mathematics, pp. 702–720,
2008.
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.” SIAM Review,
vol. 50, no. 4, Society for Industrial & Applied Mathematics, 2008, pp. 702–20,
doi:10.1137/070703235.
short: V. Kaloshin, M. Levi, SIAM Review 50 (2008) 702–720.
date_created: 2020-09-18T10:48:12Z
date_published: 2008-11-05T00:00:00Z
date_updated: 2021-01-12T08:19:46Z
day: '05'
doi: 10.1137/070703235
extern: '1'
fulldoi: https://doi.org/10.1137/070703235
intvolume: ' 50'
issue: '4'
keyword:
- Theoretical Computer Science
- Applied Mathematics
- Computational Mathematics
language:
- iso: eng
month: '11'
oa_version: None
page: 702-720
publication: SIAM Review
publication_identifier:
issn:
- 0036-1445
- 1095-7200
publication_status: published
publisher: Society for Industrial & Applied Mathematics
quality_controlled: '1'
status: public
title: Geometry of Arnold diffusion
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 50
year: '2008'
...
---
_id: '8510'
abstract:
- lang: eng
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.
article_processing_charge: No
article_type: original
author:
- first_name: Vadim
full_name: Kaloshin, Vadim
id: FE553552-CDE8-11E9-B324-C0EBE5697425
last_name: Kaloshin
orcid: 0000-0002-6051-2628
- first_name: Mark
full_name: Levi, Mark
last_name: Levi
citation:
ama: Kaloshin V, Levi M. An example of Arnold diffusion for near-integrable Hamiltonians.
Bulletin of the American Mathematical Society. 2008;45(3):409-427. doi:10.1090/s0273-0979-08-01211-1
apa: Kaloshin, V., & Levi, M. (2008). An example of Arnold diffusion for near-integrable
Hamiltonians. Bulletin of the American Mathematical Society. American Mathematical
Society. https://doi.org/10.1090/s0273-0979-08-01211-1
chicago: Kaloshin, Vadim, and Mark Levi. “An Example of Arnold Diffusion for Near-Integrable
Hamiltonians.” Bulletin of the American Mathematical Society. American
Mathematical Society, 2008. https://doi.org/10.1090/s0273-0979-08-01211-1.
ieee: V. Kaloshin and M. Levi, “An example of Arnold diffusion for near-integrable
Hamiltonians,” Bulletin of the American Mathematical Society, vol. 45,
no. 3. American Mathematical Society, pp. 409–427, 2008.
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.
mla: Kaloshin, Vadim, and Mark Levi. “An Example of Arnold Diffusion for Near-Integrable
Hamiltonians.” Bulletin of the American Mathematical Society, vol. 45,
no. 3, American Mathematical Society, 2008, pp. 409–27, doi:10.1090/s0273-0979-08-01211-1.
short: V. Kaloshin, M. Levi, Bulletin of the American Mathematical Society 45 (2008)
409–427.
date_created: 2020-09-18T10:48:20Z
date_published: 2008-07-01T00:00:00Z
date_updated: 2021-01-12T08:19:47Z
day: '01'
doi: 10.1090/s0273-0979-08-01211-1
extern: '1'
fulldoi: https://doi.org/10.1090/s0273-0979-08-01211-1
intvolume: ' 45'
issue: '3'
keyword:
- Applied Mathematics
- General Mathematics
language:
- iso: eng
month: '07'
oa_version: None
page: 409-427
publication: Bulletin of the American Mathematical Society
publication_identifier:
issn:
- 0273-0979
publication_status: published
publisher: American Mathematical Society
quality_controlled: '1'
status: public
title: An example of Arnold diffusion for near-integrable Hamiltonians
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 45
year: '2008'
...
---
_id: '8511'
abstract:
- lang: eng
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.]."
article_processing_charge: No
article_type: original
author:
- first_name: A.
full_name: Gorodetski, A.
last_name: Gorodetski
- first_name: Vadim
full_name: Kaloshin, Vadim
id: FE553552-CDE8-11E9-B324-C0EBE5697425
last_name: Kaloshin
orcid: 0000-0002-6051-2628
citation:
ama: Gorodetski A, Kaloshin V. How often surface diffeomorphisms have infinitely
many sinks and hyperbolicity of periodic points near a homoclinic tangency. Advances
in Mathematics. 2007;208(2):710-797. doi:10.1016/j.aim.2006.03.012
apa: 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. Elsevier. https://doi.org/10.1016/j.aim.2006.03.012
chicago: Gorodetski, A., and Vadim Kaloshin. “How Often Surface Diffeomorphisms
Have Infinitely Many Sinks and Hyperbolicity of Periodic Points near a Homoclinic
Tangency.” Advances in Mathematics. Elsevier, 2007. https://doi.org/10.1016/j.aim.2006.03.012.
ieee: A. Gorodetski and V. Kaloshin, “How often surface diffeomorphisms have infinitely
many sinks and hyperbolicity of periodic points near a homoclinic tangency,” Advances
in Mathematics, vol. 208, no. 2. Elsevier, pp. 710–797, 2007.
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.
mla: Gorodetski, A., and Vadim Kaloshin. “How Often Surface Diffeomorphisms Have
Infinitely Many Sinks and Hyperbolicity of Periodic Points near a Homoclinic Tangency.”
Advances in Mathematics, vol. 208, no. 2, Elsevier, 2007, pp. 710–97, doi:10.1016/j.aim.2006.03.012.
short: A. Gorodetski, V. Kaloshin, Advances in Mathematics 208 (2007) 710–797.
date_created: 2020-09-18T10:48:27Z
date_published: 2007-01-30T00:00:00Z
date_updated: 2021-01-12T08:19:47Z
day: '30'
doi: 10.1016/j.aim.2006.03.012
extern: '1'
fulldoi: https://doi.org/10.1016/j.aim.2006.03.012
intvolume: ' 208'
issue: '2'
keyword:
- General Mathematics
language:
- iso: eng
month: '01'
oa_version: None
page: 710-797
publication: Advances in Mathematics
publication_identifier:
issn:
- 0001-8708
publication_status: published
publisher: Elsevier
quality_controlled: '1'
status: public
title: How often surface diffeomorphisms have infinitely many sinks and hyperbolicity
of periodic points near a homoclinic tangency
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 208
year: '2007'
...
---
_id: '8517'
abstract:
- lang: eng
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.
article_processing_charge: No
article_type: original
author:
- first_name: Dmitry
full_name: Dolgopyat, Dmitry
last_name: Dolgopyat
- first_name: Vadim
full_name: Kaloshin, Vadim
id: FE553552-CDE8-11E9-B324-C0EBE5697425
last_name: Kaloshin
orcid: 0000-0002-6051-2628
- first_name: Leonid
full_name: Koralov, Leonid
last_name: Koralov
citation:
ama: Dolgopyat D, Kaloshin V, Koralov L. A limit shape theorem for periodic stochastic
dispersion. Communications on Pure and Applied Mathematics. 2004;57(9):1127-1158.
doi:10.1002/cpa.20032
apa: Dolgopyat, D., Kaloshin, V., & Koralov, L. (2004). A limit shape theorem
for periodic stochastic dispersion. Communications on Pure and Applied Mathematics.
Wiley. https://doi.org/10.1002/cpa.20032
chicago: Dolgopyat, Dmitry, Vadim Kaloshin, and Leonid Koralov. “A Limit Shape Theorem
for Periodic Stochastic Dispersion.” Communications on Pure and Applied Mathematics.
Wiley, 2004. https://doi.org/10.1002/cpa.20032.
ieee: D. Dolgopyat, V. Kaloshin, and L. Koralov, “A limit shape theorem for periodic
stochastic dispersion,” Communications on Pure and Applied Mathematics,
vol. 57, no. 9. Wiley, pp. 1127–1158, 2004.
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.
mla: Dolgopyat, Dmitry, et al. “A Limit Shape Theorem for Periodic Stochastic Dispersion.”
Communications on Pure and Applied Mathematics, vol. 57, no. 9, Wiley,
2004, pp. 1127–58, doi:10.1002/cpa.20032.
short: D. Dolgopyat, V. Kaloshin, L. Koralov, Communications on Pure and Applied
Mathematics 57 (2004) 1127–1158.
date_created: 2020-09-18T10:49:12Z
date_published: 2004-09-01T00:00:00Z
date_updated: 2021-01-12T08:19:50Z
day: '01'
doi: 10.1002/cpa.20032
extern: '1'
fulldoi: https://doi.org/10.1002/cpa.20032
intvolume: ' 57'
issue: '9'
keyword:
- Applied Mathematics
- General Mathematics
language:
- iso: eng
month: '09'
oa_version: None
page: 1127-1158
publication: Communications on Pure and Applied Mathematics
publication_identifier:
issn:
- 0010-3640
- 1097-0312
publication_status: published
publisher: Wiley
quality_controlled: '1'
status: public
title: A limit shape theorem for periodic stochastic dispersion
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 57
year: '2004'
...
---
_id: '8519'
article_processing_charge: No
article_type: original
author:
- first_name: Vadim
full_name: Kaloshin, Vadim
id: FE553552-CDE8-11E9-B324-C0EBE5697425
last_name: Kaloshin
orcid: 0000-0002-6051-2628
citation:
ama: Kaloshin V. The existential Hilbert 16-th problem and an estimate for cyclicity
of elementary polycycles. Inventiones mathematicae. 2003;151(3):451-512.
doi:10.1007/s00222-002-0244-9
apa: Kaloshin, V. (2003). The existential Hilbert 16-th problem and an estimate
for cyclicity of elementary polycycles. Inventiones Mathematicae. Springer
Nature. https://doi.org/10.1007/s00222-002-0244-9
chicago: Kaloshin, Vadim. “The Existential Hilbert 16-Th Problem and an Estimate
for Cyclicity of Elementary Polycycles.” Inventiones Mathematicae. Springer
Nature, 2003. https://doi.org/10.1007/s00222-002-0244-9.
ieee: V. Kaloshin, “The existential Hilbert 16-th problem and an estimate for cyclicity
of elementary polycycles,” Inventiones mathematicae, vol. 151, no. 3. Springer
Nature, pp. 451–512, 2003.
ista: Kaloshin V. 2003. The existential Hilbert 16-th problem and an estimate for
cyclicity of elementary polycycles. Inventiones mathematicae. 151(3), 451–512.
mla: Kaloshin, Vadim. “The Existential Hilbert 16-Th Problem and an Estimate for
Cyclicity of Elementary Polycycles.” Inventiones Mathematicae, vol. 151,
no. 3, Springer Nature, 2003, pp. 451–512, doi:10.1007/s00222-002-0244-9.
short: V. Kaloshin, Inventiones Mathematicae 151 (2003) 451–512.
date_created: 2020-09-18T10:49:26Z
date_published: 2003-03-01T00:00:00Z
date_updated: 2021-01-12T08:19:50Z
day: '01'
doi: 10.1007/s00222-002-0244-9
extern: '1'
fulldoi: https://doi.org/10.1007/s00222-002-0244-9
intvolume: ' 151'
issue: '3'
keyword:
- General Mathematics
language:
- iso: eng
month: '03'
oa_version: None
page: 451-512
publication: Inventiones mathematicae
publication_identifier:
issn:
- 0020-9910
- 1432-1297
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
status: public
title: The existential Hilbert 16-th problem and an estimate for cyclicity of elementary
polycycles
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 151
year: '2003'
...
---
_id: '8521'
abstract:
- lang: eng
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.
article_processing_charge: No
article_type: original
author:
- first_name: Vadim
full_name: Kaloshin, Vadim
id: FE553552-CDE8-11E9-B324-C0EBE5697425
last_name: Kaloshin
orcid: 0000-0002-6051-2628
- first_name: Brian R.
full_name: Hunt, Brian R.
last_name: Hunt
citation:
ama: Kaloshin V, Hunt BR. 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. 2001;7(5):28-36.
doi:10.1090/s1079-6762-01-00091-9
apa: Kaloshin, V., & Hunt, B. R. (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.
American Mathematical Society. https://doi.org/10.1090/s1079-6762-01-00091-9
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.” Electronic Research Announcements of the American Mathematical Society.
American Mathematical Society, 2001. https://doi.org/10.1090/s1079-6762-01-00091-9.
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,” Electronic
Research Announcements of the American Mathematical Society, vol. 7, no. 5.
American Mathematical Society, pp. 28–36, 2001.
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.
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.”
Electronic Research Announcements of the American Mathematical Society,
vol. 7, no. 5, American Mathematical Society, 2001, pp. 28–36, doi:10.1090/s1079-6762-01-00091-9.
short: V. Kaloshin, B.R. Hunt, Electronic Research Announcements of the American
Mathematical Society 7 (2001) 28–36.
date_created: 2020-09-18T10:49:43Z
date_published: 2001-04-24T00:00:00Z
date_updated: 2021-01-12T08:19:51Z
day: '24'
doi: 10.1090/s1079-6762-01-00091-9
extern: '1'
fulldoi: https://doi.org/10.1090/s1079-6762-01-00091-9
intvolume: ' 7'
issue: '5'
keyword:
- General Mathematics
language:
- iso: eng
month: '04'
oa_version: None
page: 28-36
publication: Electronic Research Announcements of the American Mathematical Society
publication_identifier:
issn:
- 1079-6762
publication_status: published
publisher: American Mathematical Society
quality_controlled: '1'
status: public
title: A stretched exponential bound on the rate of growth of the number of periodic
points for prevalent diffeomorphisms II
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 7
year: '2001'
...
---
_id: '8522'
abstract:
- lang: eng
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.
article_processing_charge: No
article_type: original
author:
- first_name: Vadim
full_name: Kaloshin, Vadim
id: FE553552-CDE8-11E9-B324-C0EBE5697425
last_name: Kaloshin
orcid: 0000-0002-6051-2628
- first_name: Brian R.
full_name: Hunt, Brian R.
last_name: Hunt
citation:
ama: Kaloshin V, Hunt BR. 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. 2001;7(4):17-27. doi:10.1090/s1079-6762-01-00090-7
apa: Kaloshin, V., & Hunt, B. R. (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.
American Mathematical Society. https://doi.org/10.1090/s1079-6762-01-00090-7
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.” Electronic Research Announcements of the American Mathematical Society.
American Mathematical Society, 2001. https://doi.org/10.1090/s1079-6762-01-00090-7.
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,” Electronic
Research Announcements of the American Mathematical Society, vol. 7, no. 4.
American Mathematical Society, pp. 17–27, 2001.
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.
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.” Electronic
Research Announcements of the American Mathematical Society, vol. 7, no. 4,
American Mathematical Society, 2001, pp. 17–27, doi:10.1090/s1079-6762-01-00090-7.
short: V. Kaloshin, B.R. Hunt, Electronic Research Announcements of the American
Mathematical Society 7 (2001) 17–27.
date_created: 2020-09-18T10:49:56Z
date_published: 2001-04-18T00:00:00Z
date_updated: 2021-01-12T08:19:51Z
day: '18'
doi: 10.1090/s1079-6762-01-00090-7
extern: '1'
fulldoi: https://doi.org/10.1090/s1079-6762-01-00090-7
intvolume: ' 7'
issue: '4'
keyword:
- General Mathematics
language:
- iso: eng
month: '04'
oa_version: None
page: 17-27
publication: Electronic Research Announcements of the American Mathematical Society
publication_identifier:
issn:
- 1079-6762
publication_status: published
publisher: American Mathematical Society
quality_controlled: '1'
status: public
title: A stretched exponential bound on the rate of growth of the number of periodic
points for prevalent diffeomorphisms I
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 7
year: '2001'
...
---
_id: '11683'
abstract:
- lang: eng
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.
article_processing_charge: No
article_type: original
author:
- first_name: Monika H
full_name: Henzinger, Monika H
id: 540c9bbd-f2de-11ec-812d-d04a5be85630
last_name: Henzinger
orcid: 0000-0002-5008-6530
- first_name: Satish
full_name: Rao, Satish
last_name: Rao
- first_name: Harold N.
full_name: Gabow, Harold N.
last_name: Gabow
citation:
ama: 'Henzinger M, Rao S, Gabow HN. Computing vertex connectivity: New bounds from
old techniques. Journal of Algorithms. 2000;34(2):222-250. doi:10.1006/jagm.1999.1055'
apa: 'Henzinger, M., Rao, S., & Gabow, H. N. (2000). Computing vertex connectivity:
New bounds from old techniques. Journal of Algorithms. Elsevier. https://doi.org/10.1006/jagm.1999.1055'
chicago: 'Henzinger, Monika, Satish Rao, and Harold N. Gabow. “Computing Vertex
Connectivity: New Bounds from Old Techniques.” Journal of Algorithms. Elsevier,
2000. https://doi.org/10.1006/jagm.1999.1055.'
ieee: 'M. Henzinger, S. Rao, and H. N. Gabow, “Computing vertex connectivity: New
bounds from old techniques,” Journal of Algorithms, vol. 34, no. 2. Elsevier,
pp. 222–250, 2000.'
ista: 'Henzinger M, Rao S, Gabow HN. 2000. Computing vertex connectivity: New bounds
from old techniques. Journal of Algorithms. 34(2), 222–250.'
mla: 'Henzinger, Monika, et al. “Computing Vertex Connectivity: New Bounds from
Old Techniques.” Journal of Algorithms, vol. 34, no. 2, Elsevier, 2000,
pp. 222–50, doi:10.1006/jagm.1999.1055.'
short: M. Henzinger, S. Rao, H.N. Gabow, Journal of Algorithms 34 (2000) 222–250.
date_created: 2022-07-28T08:56:10Z
date_published: 2000-02-01T00:00:00Z
date_updated: 2024-11-04T11:42:08Z
day: '01'
doi: 10.1006/jagm.1999.1055
extern: '1'
fulldoi: https://doi.org/10.1006/jagm.1999.1055
intvolume: ' 34'
issue: '2'
keyword:
- Computational Theory and Mathematics
- Computational Mathematics
- Control and Optimization
language:
- iso: eng
month: '02'
oa_version: None
page: 222-250
publication: Journal of Algorithms
publication_identifier:
issn:
- 0196-6774
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Computing vertex connectivity: New bounds from old techniques'
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 34
year: '2000'
...
---
_id: '8527'
abstract:
- lang: eng
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.
article_processing_charge: No
article_type: original
author:
- first_name: Brian R
full_name: Hunt, Brian R
last_name: Hunt
- first_name: Vadim
full_name: Kaloshin, Vadim
id: FE553552-CDE8-11E9-B324-C0EBE5697425
last_name: Kaloshin
orcid: 0000-0002-6051-2628
citation:
ama: Hunt BR, Kaloshin V. How projections affect the dimension spectrum of fractal
measures. Nonlinearity. 1997;10(5):1031-1046. doi:10.1088/0951-7715/10/5/002
apa: Hunt, B. R., & Kaloshin, V. (1997). How projections affect the dimension
spectrum of fractal measures. Nonlinearity. IOP Publishing. https://doi.org/10.1088/0951-7715/10/5/002
chicago: Hunt, Brian R, and Vadim Kaloshin. “How Projections Affect the Dimension
Spectrum of Fractal Measures.” Nonlinearity. IOP Publishing, 1997. https://doi.org/10.1088/0951-7715/10/5/002.
ieee: B. R. Hunt and V. Kaloshin, “How projections affect the dimension spectrum
of fractal measures,” Nonlinearity, vol. 10, no. 5. IOP Publishing, pp.
1031–1046, 1997.
ista: Hunt BR, Kaloshin V. 1997. How projections affect the dimension spectrum of
fractal measures. Nonlinearity. 10(5), 1031–1046.
mla: Hunt, Brian R., and Vadim Kaloshin. “How Projections Affect the Dimension Spectrum
of Fractal Measures.” Nonlinearity, vol. 10, no. 5, IOP Publishing, 1997,
pp. 1031–46, doi:10.1088/0951-7715/10/5/002.
short: B.R. Hunt, V. Kaloshin, Nonlinearity 10 (1997) 1031–1046.
date_created: 2020-09-18T10:50:41Z
date_published: 1997-06-19T00:00:00Z
date_updated: 2021-01-12T08:19:53Z
day: '19'
doi: 10.1088/0951-7715/10/5/002
extern: '1'
fulldoi: https://doi.org/10.1088/0951-7715/10/5/002
intvolume: ' 10'
issue: '5'
keyword:
- Mathematical Physics
- General Physics and Astronomy
- Applied Mathematics
- Statistical and Nonlinear Physics
language:
- iso: eng
month: '06'
oa_version: None
page: 1031-1046
publication: Nonlinearity
publication_identifier:
issn:
- 0951-7715
- 1361-6544
publication_status: published
publisher: IOP Publishing
quality_controlled: '1'
status: public
title: How projections affect the dimension spectrum of fractal measures
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 10
year: '1997'
...