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
   • On decay of correlations in Anosov flows , Ann. of Math. 147 (1998) 357-390.
   • Prevalence of rapid mixing:
     Part I : Ergodic Theory and Dynamical Systems 18 (1998) 1097-1114.
     Part II : Ergodic Theory and Dynamical Systems 20 (2000) 1045-1059.
   • On dynamics of mostly contracting diffeomorphisms , Comm. in Math. Physics , 213 (2000) 181-201.
   • On mixing properties of compact group extensions of hyperbolic systems , Israel J. Math. , 130 (2002) 157-205.
5. Every compact manifold carries a complitely hyperbolic diffeomorphism , (with Yakov Pesin ), Ergodic Theory and Dynamical Systems , 22 (2002) 409-437.
6. Stable accessibility is C1 dense , (with Amie Wilkinson ), Asterisque 287 (2003), 33-60.
7. Limit Theorems for partially hyperbolic systems , Transactions of the AMS 356 (2004) 1637-1689.
8. Perturbation Theory for Invariant measures
   • On differentiability of SRB states for partially hyperbolic systems , Invent. Math. 155 (2004) 389--449.
   • Averaging and Invariant measures , Moscow Math. J. 5 (2005) 537-576.
   • Prelude to a kiss , in Modern dynamical systems (edited by Misha Brin , Boris Hasselblatt and Yakov Pesin ), Cambridge Unversity Press, 2004, 313-324.
   • Anomalous current in periodic Lorentz gases with infinite horizon (with Nikolai Chernov ), Russian Math. Surveys 64 (2009) 651-699.
   • The diffusion coefficient for piecewise expanding maps of the interval with metastable states (with Paul Wright ), Stochastics and Dynamics 12 (2012) paper 1150005.
9. Dynamics of Stochastic Flows (with Vadim Kaloshin and Leonid Koralov)
   • Sample path properties of stochastic flows , Ann. Prob. , 32 (2004) 1-27.
   • Hausdorff Dimension in Stochastic Dispersion , J. Stat. Phys. , 108 (2002) 943-971.
   • A limit shape theorem for periodic stochastic dispersion , CPAM , 57 (2004) 1127-1158.
10. Livsic theory for compact group extensions of hyperbolic systems , Moscow Math. J. 5 (2005) 55-66.
11. On simultaneous linearization of diffeomorphisms of the sphere , (with Raphael Krikorian ), Duke Math. J. , 136 (2007) 475-505.
12. Evolution of adiabatic invariants in stochastic averaging , Stochastics and Dynamics 4 (2004) 265-275.
13. Brownian Brownian Motion-1, (with Nikolai Chernov ), Memoirs AMS, vol. 198, no 927 (2009).
14. Small random perturbations of area preserving flows
    • Avergaging of Hamiltonian flows with an ergodic component , (with Leonid Koralov), Ann. Prob. 36 (2008) 1999-2049.
    • Deterministic and stochastic perturbations of area preserving flows on a two-dimensional torus , (with Mark Freidlin and Leonid Koralov), Ergodic Theory and Dynamical Systems , 32 (2012) 899-918.
    • Averaging of incompressible flows on two-dimensional surfaces , (with Leonid Koralov), to appear in Journal AMS .
15. Dynamics of Lorentz gas (with Domokos Szasz and Tamas Varju)
    • Recurrence properties of Lorentz gas , Duke Math. J. 142 (2008) 241-281.
    • Limit Theorems for Locally Perturbed Lorentz processes , Duke Math. J. 148 (2009) 459-499.
16. Fermi acceleration
    • Bouncing balls in non-linear potentials , Discrete and Continuous Dynamical Systems - A 22 (2008) 165-182.
    • Galton board: Limit Theorems and Recurrence , (with Nikolai Chernov ), Journal AMS 22 (2009) 821-858.
    • Motion in a random force field , (with Leonid Koralov ), Nonlinearity 22 (2009) 187-211.
    • Unbounded orbits for semicircular outer billiard , (with Bassam Fayad), Annales Henri Poincare 10 (2009) 357-375.
    • Dynamics of some piecewise smooth Fermi-Ulam Models , (with Jacopo de Simoi), Chaos 22 (2012) paper 026124.
17. Particle's drift in self-similar billiards, (with Nikolai Chernov ), Ergodic Theory and Dynamical Systems 28 (2008) 389-403.
18. Repulsion from Resonances , Memoires SMF 128 (2012).
19. Energy transfer in a fast-slow Hamiltonian system (with Carlangelo Liverani ), Comm. Math. Phys. 308 (2011) 201-225.
20. Limit theorems for dispersing billiards with cusps (with Peter Balint and Nikolai Chernov ), Comm. Math. Phys. 308 (2011) 479-510.
21. Random walks in random environment
    • Random walks in Markovian enviroment , (with Carlangelo Liverani ), Elecronic Comm. Prob. 14 (2009) 245-251.
    • Quenched limit theorems for nearest neighbor random walk in 1D random environment, (with Ilya Goldsheid ), Comm. Math. Phys. 315 (2012) 241-277.
    • Limit theorems for random walks on a strip in subdiffusive regime, (with Ilya Goldsheid ), Nonlinearity 26 (2013) 1743-1782.
    • Local limit theorems for random walk in 1D random environment, (with Ilya Goldsheid ), to appear in Arxiv der Mathematik.
22. Excited random walks
    • Central Limit Theorem for Excited Random Walk in the Recurrent Regime, ALEA 8 (2011) 259-268.
    • Scaling limits of recurrent excited random walks on integers , (with Elena Kosygina ), Elecronic Comm. Prob. 17 (2012) paper 35.
23. Convergence of moments for dispersing billiards with cusps , (with Peter Balint and Nikolai Chernov ), preprint.
24. Deviations of Ergodic sums for Toral Translations (with Bassam Fayad), part I , part II , preprints.

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.