De Simoi, Jacopo, et al. “Marked Length Spectral Determination of Analytic Chaotic Billiards with Axial Symmetries.”10.1007/s00222-023-01191-8__Inventiones Mathematicae, vol. 233, Springer Nature, 2023, pp. 829–901, doi:10.1007/s00222-023-01191-8.

Chen, Jianyu, et al. “Length Spectrum Rigidity for Piecewise Analytic Bunimovich Billiards.”10.1007/s00220-023-04837-z__Communications in Mathematical Physics, Springer Nature, 2023, doi:10.1007/s00220-023-04837-z.

Koudjinan, Edmond, and Vadim Kaloshin. “On Some Invariants of Birkhoff Billiards under Conjugacy.”10.1134/S1560354722050021__Regular and Chaotic Dynamics, vol. 27, no. 6, Springer Nature, 2022, pp. 525–37, doi:10.1134/S1560354722050021.

Kaloshin, Vadim, and Edmond Koudjinan. Non Co-Preservation of the 1/2 and  1/(2l+1)-Rational Caustics along Deformations of Circles. 2021.

Kaloshin, Vadim, and Ke Zhang. Arnold Diffusion for Smooth Systems of Two and a Half Degrees of Freedom. 1st ed., vol. 208, Princeton University Press, 2020, doi:10.1515/9780691204932.

Bálint, Péter, et al. “Marked Length Spectrum, Homoclinic Orbits and the Geometry of Open Dispersing Billiards.”10.1007/s00220-019-03448-x__Communications in Mathematical Physics, vol. 374, no. 3, Springer Nature, 2019, pp. 1531–75, doi:10.1007/s00220-019-03448-x.

Guardia, Marcel, et al. “Asymptotic Density of Collision Orbits in the Restricted Circular Planar 3 Body Problem.”10.1007/s00205-019-01368-7__Archive for Rational Mechanics and Analysis, vol. 233, no. 2, Springer Nature, 2019, pp. 799–836, doi:10.1007/s00205-019-01368-7.

Huang, Guan, and Vadim Kaloshin. “On the Finite Dimensionality of Integrable Deformations of Strictly Convex Integrable Billiard Tables.”10.17323/1609-4514-2019-19-2-307-327__Moscow Mathematical Journal, vol. 19, no. 2, American Mathematical Society, 2019, pp. 307–27, doi:10.17323/1609-4514-2019-19-2-307-327.

Delshams, Amadeu, et al. “Global Instability in the Restricted Planar Elliptic Three Body Problem.”10.1007/s00220-018-3248-z__Communications in Mathematical Physics, vol. 366, no. 3, Springer Nature, 2018, pp. 1173–228, doi:10.1007/s00220-018-3248-z.

Huang, Guan, et al. “Nearly Circular Domains Which Are Integrable Close to the Boundary Are Ellipses.”10.1007/s00039-018-0440-4__Geometric and Functional Analysis, vol. 28, no. 2, Springer Nature, 2018, pp. 334–92, doi:10.1007/s00039-018-0440-4.

Kaloshin, Vadim, and Alfonso Sorrentino. “On the Local Birkhoff Conjecture for Convex Billiards.”10.4007/annals.2018.188.1.6__Annals of Mathematics, vol. 188, no. 1, Annals of Mathematics, Princeton U, 2018, pp. 315–80, doi:10.4007/annals.2018.188.1.6.

Kaloshin, Vadim, and Alfonso Sorrentino. “On the Integrability of Birkhoff Billiards.”10.1098/rsta.2017.0419__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.

Kaloshin, Vadim, and Ke Zhang. “Density of Convex Billiards with Rational Caustics.”10.1088/1361-6544/aadc12__Nonlinearity, vol. 31, no. 11, IOP Publishing, 2018, pp. 5214–34, doi:10.1088/1361-6544/aadc12.

Buhovsky, Lev, and Vadim Kaloshin. “Nonisometric Domains with the Same Marvizi-Melrose Invariants.”10.1134/s1560354718010057__Regular and Chaotic Dynamics, vol. 23, Springer Nature, 2018, pp. 54–59, doi:10.1134/s1560354718010057.

Huang, Guan, et al. “On the Marked Length Spectrum of Generic Strictly Convex Billiard Tables.”10.1215/00127094-2017-0038__Duke Mathematical Journal, vol. 167, no. 1, Duke University Press, 2017, pp. 175–209, doi:10.1215/00127094-2017-0038.

De Simoi, Jacopo, et al. “Dynamical Spectral Rigidity among Z2-Symmetric Strictly Convex Domains Close to a Circle.”10.4007/annals.2017.186.1.7__Annals of Mathematics, vol. 186, no. 1, Annals of Mathematics, 2017, pp. 277–314, doi:10.4007/annals.2017.186.1.7.

Féjoz, Jacques, et al. “Kirkwood Gaps and Diffusion along Mean Motion Resonances in the Restricted Planar Three-Body Problem.”10.4171/jems/642__Journal of the European Mathematical Society, vol. 18, no. 10, European Mathematical Society Publishing House, 2016, pp. 2315–403, doi:10.4171/jems/642.

Avila, Artur, et al. “An Integrable Deformation of an Ellipse of Small Eccentricity Is an Ellipse.”10.4007/annals.2016.184.2.5__Annals of Mathematics, vol. 184, no. 2, Princeton University Press, 2016, pp. 527–58, doi:10.4007/annals.2016.184.2.5.

Guardia, M., et al. “A Second Order Expansion of the Separatrix Map for Trigonometric Perturbations of a Priori Unstable Systems.”10.1007/s00220-016-2705-9__Communications in Mathematical Physics, vol. 348, Springer Nature, 2016, pp. 321–61, doi:10.1007/s00220-016-2705-9.

Bernard, Patrick, et al. “Arnold Diffusion in Arbitrary Degrees of Freedom and Normally Hyperbolic Invariant Cylinders.”10.1007/s11511-016-0141-5__Acta Mathematica, vol. 217, no. 1, Institut Mittag-Leffler, 2016, pp. 1–79, doi:10.1007/s11511-016-0141-5.

Kaloshin, Vadim, and K. Zhang. “Arnold Diffusion for Smooth Convex Systems of Two and a Half Degrees of Freedom.”10.1088/0951-7715/28/8/2699__Nonlinearity, vol. 28, no. 8, IOP Publishing, 2015, pp. 2699–720, doi:10.1088/0951-7715/28/8/2699.

Guardia, Marcel, and Vadim Kaloshin. “Growth of Sobolev Norms in the Cubic Defocusing Nonlinear Schrödinger Equation.”10.4171/jems/499__Journal of the European Mathematical Society, vol. 17, no. 1, European Mathematical Society Publishing House, 2015, pp. 71–149, doi:10.4171/jems/499.

Bounemoura, Abed, and Vadim Kaloshin. “A Note on Micro-Instability for Hamiltonian Systems Close to Integrable.”10.1090/proc/12796__Proceedings of the American Mathematical Society, vol. 144, no. 4, American Mathematical Society, 2015, pp. 1553–60, doi:10.1090/proc/12796.

Bounemoura, Abed, and Vadim Kaloshin. “Generic Fast Diffusion for a Class of Non-Convex Hamiltonians with Two Degrees of Freedom.”10.17323/1609-4514-2014-14-2-181-203__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.

Kaloshin, Vadim, et al. “Arnold Diffusion in a Pendulum Lattice.”10.1002/cpa.21509__Communications on Pure and Applied Mathematics, vol. 67, no. 5, Wiley, 2014, pp. 748–75, doi:10.1002/cpa.21509.

Kaloshin, Vadim, and Maria Saprykina. “An Example of a Nearly Integrable Hamiltonian System with a Trajectory Dense in a Set of Maximal Hausdorff Dimension.”10.1007/s00220-012-1532-x__Communications in Mathematical Physics, vol. 315, no. 3, Springer Nature, 2012, pp. 643–97, doi:10.1007/s00220-012-1532-x.

Kaloshin, Vadim, and O. S. KOZLOVSKI. “A Cr Unimodal Map with an Arbitrary Fast Growth of the Number of Periodic Points.”10.1017/s0143385710000817__Ergodic Theory and Dynamical Systems, vol. 32, no. 1, Cambridge University Press, 2012, pp. 159–65, doi:10.1017/s0143385710000817.

Albouy, Alain, and Vadim Kaloshin. “Finiteness of Central Configurations of Five Bodies in the Plane.”10.4007/annals.2012.176.1.10__Annals of Mathematics, vol. 176, no. 1, Princeton University Press, 2012, pp. 535–88, doi:10.4007/annals.2012.176.1.10.

Galante, Joseph, and Vadim Kaloshin. “Destruction of Invariant Curves in the Restricted Circular Planar Three-Body Problem by Using Comparison of Action.”10.1215/00127094-1415878__Duke Mathematical Journal, vol. 159, no. 2, Duke University Press, 2011, pp. 275–327, doi:10.1215/00127094-1415878.

Kaloshin, Vadim, et al. “Almost Dense Orbit on Energy Surface.”10.1142/9789814304634_0017__XVIth International Congress on Mathematical Physics, World Scientific, 2010, pp. 314–22, doi:10.1142/9789814304634_0017.

Hunt, Brian R., and Vadim Kaloshin. “Prevalence.”10.1016/s1874-575x(10)00310-3__Handbook of Dynamical Systems, vol. 3, Elsevier, 2010, pp. 43–87, doi:10.1016/s1874-575x(10)00310-3.

Gorodetski, Anton, and Vadim Kaloshin. “Conservative Homoclinic Bifurcations and Some Applications.”10.1134/s0081543809040063__Proceedings of the Steklov Institute of Mathematics, vol. 267, no. 1, Springer Nature, 2009, pp. 76–90, doi:10.1134/s0081543809040063.

Kaloshin, Vadim, and Mark Levi. “An Example of Arnold Diffusion for Near-Integrable Hamiltonians.”10.1090/s0273-0979-08-01211-1__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.

Kaloshin, Vadim, and Mark Levi. “Geometry of Arnold Diffusion.”10.1137/070703235__SIAM Review, vol. 50, no. 4, Society for Industrial &; Applied Mathematics, 2008, pp. 702–20, doi:10.1137/070703235.

Gorodetski, A., and Vadim Kaloshin. “How Often Surface Diffeomorphisms Have Infinitely Many Sinks and Hyperbolicity of Periodic Points near a Homoclinic Tangency.”10.1016/j.aim.2006.03.012__Advances in Mathematics, vol. 208, no. 2, Elsevier, 2007, pp. 710–97, doi:10.1016/j.aim.2006.03.012.

Kaloshin, Vadim, and Brian Hunt. “Stretched Exponential Estimates on Growth of the Number of Periodic Points for Prevalent Diffeomorphisms I.”10.4007/annals.2007.165.89__Annals of Mathematics, vol. 165, no. 1, Princeton University Press, 2007, pp. 89–170, doi:10.4007/annals.2007.165.89.

OTT, WILLIAM, et al. “The Effect of Projections on Fractal Sets and Measures in Banach Spaces.”10.1017/s0143385705000714__Ergodic Theory and Dynamical Systems, vol. 26, no. 3, Cambridge University Press, 2006, pp. 869–91, doi:10.1017/s0143385705000714.

Kaloshin, Vadim, et al. “Long Time Behaviour of Periodic Stochastic Flows.”10.1142/9789812704016_0026__XIVth International Congress on Mathematical Physics, World Scientific, 2006, pp. 290–95, doi:10.1142/9789812704016_0026.

Kaloshin, Vadim, and Maria Saprykina. “Generic 3-Dimensional Volume-Preserving Diffeomorphisms with Superexponential Growth of Number of Periodic Orbits.”10.3934/dcds.2006.15.611__Discrete &; Continuous Dynamical Systems - A, vol. 15, no. 2, American Institute of Mathematical Sciences (AIMS), 2006, pp. 611–40, doi:10.3934/dcds.2006.15.611.

Bourgain, Jean, and Vadim Kaloshin. “On Diffusion in High-Dimensional Hamiltonian Systems.”10.1016/j.jfa.2004.09.006__Journal of Functional Analysis, vol. 229, no. 1, Elsevier, 2005, pp. 1–61, doi:10.1016/j.jfa.2004.09.006.

Dolgopyat, Dmitry, et al. “A Limit Shape Theorem for Periodic Stochastic Dispersion.”10.1002/cpa.20032__Communications on Pure and Applied Mathematics, vol. 57, no. 9, Wiley, 2004, pp. 1127–58, doi:10.1002/cpa.20032.

Koralov, Leonid, et al. “Sample Path Properties of the Stochastic Flows.”10.1214/aop/1078415827__The Annals of Probability, vol. 32, no. 1A, Institute of Mathematical Statistics, 2004, pp. 1–27, doi:10.1214/aop/1078415827.

Kaloshin, Vadim. “The Existential Hilbert 16-Th Problem and an Estimate for Cyclicity of Elementary Polycycles.”10.1007/s00222-002-0244-9__Inventiones Mathematicae, vol. 151, no. 3, Springer Nature, 2003, pp. 451–512, doi:10.1007/s00222-002-0244-9.

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.”10.1090/s1079-6762-01-00090-7__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.

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.”10.1090/s1079-6762-01-00091-9__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.

Kaloshin, Vadim, and I. Rodnianski. “Diophantine Properties of Elements of SO(3).”10.1007/s00039-001-8222-8__Geometric And Functional Analysis, vol. 11, no. 5, Springer Nature, 2001, pp. 953–70, doi:10.1007/s00039-001-8222-8.

Kaloshin, Vadim. “Generic Diffeomorphisms with Superexponential Growth of Number of Periodic Orbits.”10.1007/s002200050811__Communications in Mathematical Physics, vol. 211, Springer Nature, 2000, pp. 253–71, doi:10.1007/s002200050811.

Kaloshin, Vadim. “An Extension of the Artin-Mazur Theorem.”10.2307/121093__The Annals of Mathematics, vol. 150, no. 2, JSTOR, 1999, pp. 729–41, doi:10.2307/121093.

Kaloshin, Vadim. “Prevalence in the Space of Finitely Smooth Maps.”10.1007/bf02466014__Functional Analysis and Its Applications, vol. 31, no. 2, Springer Nature, 1997, pp. 95–99, doi:10.1007/bf02466014.

Hunt, Brian R., and Vadim Kaloshin. “How Projections Affect the Dimension Spectrum of Fractal Measures.”10.1088/0951-7715/10/5/002__Nonlinearity, vol. 10, no. 5, IOP Publishing, 1997, pp. 1031–46, doi:10.1088/0951-7715/10/5/002.