Dmitry Dolgopyat's home page

Some papers and preprints.

Research

  1. Multifractal properties of sets of zeroes of Brownian path , (with Vadim Sidorov) Fundamenta Mathematicae 147 (1995) 157-171.
  2. Bounded orbits of Anosov flows , Duke Math. J. 87 (1997) 87-114.
  3. Entropy of coupled map lattices , J. Stat. Phys. 86 (1997) 377-389.
  4. Decay of Correlations
  5. Mostly contracting diffeomorphisms
  6. Every compact manifold carries a complitely hyperbolic diffeomorphism , (with Yakov Pesin ), Ergodic Theory and Dynamical Systems , 22 (2002) 409-437.
  7. Stable accessibility is C1 dense , (with Amie Wilkinson ), Asterisque 287 (2003), 33-60.
  8. Limit Theorems for partially hyperbolic systems , Transactions of the AMS 356 (2004) 1637-1689.
  9. Perturbation Theory for Invariant measures
  10. Dynamics of Stochastic Flows (with Vadim Kaloshin and Leonid Koralov)
  11. Livsic theory for compact group extensions of hyperbolic systems , Moscow Math. J. 5 (2005) 55-66.
  12. On simultaneous linearization of diffeomorphisms of the sphere , (with Raphael Krikorian ), Duke Math. J. , 136 (2007) 475-505.
  13. Evolution of adiabatic invariants in stochastic averaging , Stochastics and Dynamics 4 (2004) 265-275.
  14. Brownian Brownian Motion-1, (with Nikolai Chernov ), Memoirs AMS, vol. 198, no 927 (2009).
  15. Small random perturbations of area preserving flows
  16. Dynamics of Lorentz gas
  17. Fermi acceleration
  18. Particle's drift in self-similar billiards, (with Nikolai Chernov ), Ergodic Theory and Dynamical Systems 28 (2008) 389-403.
  19. Repulsion from Resonances , Memoires SMF 128 (2012).
  20. Energy transfer in a fast-slow Hamiltonian system (with Carlangelo Liverani ), Comm. Math. Phys. 308 (2011) 201-225.
  21. Limit theorems for dispersing billiards with cusps (with Peter Balint and Nikolai Chernov ), Comm. Math. Phys. 308 (2011) 479-510.
  22. Random walks in random environment
  23. Excited random walks
  24. Convergence of moments for dispersing billiards with cusps , (with Peter Balint and Nikolai Chernov ), Contemporary Mathematics 698 (2017) 35-67.
  25. Dynamics of toral translations
  26. Noncollision singularities in the planar two-center-two-body problem, with Jinxin Xue , Comm. in Math. Physics 345 (2016) 797-879.
  27. Asymptotic expansions in Central Limit Theorem
  28. On small gaps in the length spectrum, with Dmitry Jakobson , Journal of Modern Dynamics 10 (2016) 339-352.
  29. Central limit theorems for simultaneous Diophantine approximations , (with Bassam Fayad and Ilya Vinogradov ), J. de l'Ecole Polytechnique 4 (2017) 1-35.
  30. Temporal Limit Theorems (witt Omri Sarig )
  31. Multi-type branching processes with time-dependent branching rates (with Pratima Hebbar, Lenid Koralov, and Mark Perlman), J. of Appl. Probability 55 (2018) 701-727.
  32. Infinite measure mixing for some mechanical systems (with Peter Nandori ), Adv. Math. . 410 (2022) paper no. 108757.
  33. Global observables for random walks: law of large numbers (with Marco Lenci and Peter Nandori ) Annales Institut Henri Poincare Prob. Stat. 57 (2021) 94-115.
  34. Multiple Borel Cantelli Lemma in dynamics and multilog law for recurrence (with Bassam Fayad and Sixu Liu), Journal of Modern Dynamics 18 (2022) 209-289.
  35. On dynamics of generalized (T, T^{-1}) transformations of generalized (T, T^{-1}) transformations
  36. Exponential mixing implies Bernoulli with Adam Kanigowski and Federico Rodriguez Hertz, to appear in Ann. Math.

Expositiory

  1. Addendum to the paper Periodic points and dynamical spectra , by Viviane Baladi (with Mark Pollicott ) Ergodic Theory and Dynamical Systems 18 (1998) 293-301.
  2. Addendum to the paper Lectures on Lyapunov exponents and smooth ergodic theory by Luis Barreira and Yakov Pesin (with Hyui Hu and Yakov Pesin ), Proceedings of Symposia in Pure Mathematics 69 (2001) 95-106.
  3. Lectures on u-Gibbs states , Evanston, May 31-June 2, 2001.
  4. Sample path properties of random transformations , Kyoto, August 12, 2002,
  5. Introduction to averaging , Institut Henri Poincare, april-july 2005.
  6. Stable ergodicity for partially hyperbolic attractors with negative central exponents , (with Keith Burns , Yakov Pesin and Mark Pollicott ), J. Modern Dynamics 2 (2008) 63-81.
  7. Hyperbolic billiards and statistical physics , (with Nikolai Chernov ), ICM, Madrid, August 2006.
  8. Diffusive motion and recurrence on generalized Galton board , (with Nikolai Chernov ), Phys. Rev. Lett. , 99 (2007) paper 030601.
  9. Fermi acceleration , Canadian Mathematical Society Winter Meeting. December 2006.
  10. Limit Theorems for Hyperbolic Systems, Beijing, August 2009.
  11. Piecewise smooth perturbations of integrable systems, International Congress of Mathematical Physics, Aalborg, Denmark, August 2012.
  12. Lectures on Bouncing Balls, Murcia, Spain, January 2013.
  13. Limit theorems for toral translations (with Bassam Fayad), Lousagne, June 2013.
  14. Notes on Bjorklund-Gorodnik Central Limit Thereom .
Some people say: Blessed are actors and singers for their art is not preserved. (Akutagawa)