** Research **

- Multifractal properties of sets of zeroes of Brownian path , (with Vadim Sidorov) Fundamenta Mathematicae 147 (1995) 157-171.
- Bounded orbits of Anosov flows , Duke Math. J. 87 (1997) 87-114.
- Entropy of coupled map lattices , J. Stat. Phys. 86 (1997) 377-389.
- 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 mixing properties of compact group extensions of hyperbolic systems , Israel J. Math. , 130 (2002) 157-205.

- Mostly contracting diffeomorphisms
- On dynamics of mostly contracting diffeomorphisms , Comm. in Math. Physics , 213 (2000) 181-201.
- Geometric and measure-theoretical structures of maps with mostly contracting center , (with Marcelo Viana and Jiagang Yang), Comm. in Math. Physics 341 (2016) 991-1014.

- Every compact manifold carries a complitely hyperbolic diffeomorphism , (with Yakov Pesin ), Ergodic Theory and Dynamical Systems , 22 (2002) 409-437.
- Stable accessibility is C1 dense , (with Amie Wilkinson ), Asterisque 287 (2003), 33-60.
- Limit Theorems for partially hyperbolic systems , Transactions of the AMS 356 (2004) 1637-1689.
- 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.
- Regularity of absolutely continuous invariant measures for piecewise expanding unimodal maps , (with Fabian Contreras), to appear in Nonlinearity .

- 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.

- Livsic theory for compact group extensions of hyperbolic systems , Moscow Math. J. 5 (2005) 55-66.
- On simultaneous linearization of diffeomorphisms of the sphere , (with Raphael Krikorian ), Duke Math. J. , 136 (2007) 475-505.
- Evolution of adiabatic invariants in stochastic averaging , Stochastics and Dynamics 4 (2004) 265-275.
- Brownian Brownian Motion-1, (with Nikolai Chernov ), Memoirs AMS, vol. 198, no 927 (2009).
- 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), Journal AMS 26 (2013) 427-449.

- Dynamics of Lorentz gas
- Recurrence properties of Lorentz gas (with Domokos Szasz and Tamas Varju), Duke Math. J. 142 (2008) 241-281.
- Limit Theorems for Locally Perturbed Lorentz processes (with Domokos Szasz and Tamas Varju), Duke Math. J. 148 (2009) 459-499.
- Non equilibrium density profiles in Lorentz tubes with thermostated boundaries, (with Peter Nandori ) CPAM 69 (2016) 649-692.

- 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 ), Annales Henri Poincare 10 (2009) 357-375.
- Dynamics of some piecewise smooth Fermi-Ulam Models , (with Jacopo de Simoi ), Chaos 22 (2012) paper 026124.

- Particle's drift in self-similar billiards, (with Nikolai Chernov ), Ergodic Theory and Dynamical Systems 28 (2008) 389-403.
- Repulsion from Resonances , Memoires SMF 128 (2012).
- Energy transfer in a fast-slow Hamiltonian system (with Carlangelo Liverani ), Comm. Math. Phys. 308 (2011) 201-225.
- Limit theorems for dispersing billiards with cusps (with Peter Balint and Nikolai Chernov ), Comm. Math. Phys. 308 (2011) 479-510.
- 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 ), Arxiv der Mathematik 101 (2013) 191-200.
- Central Limit Theorem for recurrent random walks on a strip with bounded potential, (with Ilya Goldsheid ), preprint.

- 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.
- Excursions and occupation times of critical excited random walks , (with Elena Kosygina ), ALEA 12 (2015) 427-450.

- Convergence of moments for dispersing billiards with cusps , (with Peter Balint and Nikolai Chernov ), preprint.
- Dynamics of toral translations
- Deviations of Ergodic sums for Toral Translations (with Bassam Fayad), part I , GAFA 24 (2014) 85-115, part II , preprint.
- The visits to zero of a random walk driven by an irrational rotation, (with Artur Avila , Eduard Duriev and Omri Sarig ), Israel J. Math. 207 (2015) 653-717.

- Noncollision singularities in the planar two-center-two-body problem, with Jinxin Xue Comm. in Math. Physics 345 (2016) 797-879.
- A Local Limit Theorem for sum of independent random vectors , Electronic J. Prob. 21 (2016) paper 39.
- On small gaps in the length spectrum, with Dmitry Jakobson , Journal of Modern Dynamics 10 (2016) 339-352.
- Central limit theorems for simultaneous Diophantine approximations , (with Bassam Fayad and Ilya Vinogradov ), J. de l'Ecole Polytechnique 4 (2017) 1-35.
- Temporal Distributional Limit Theorems for Dynamical Systems (with Omri Sarig ), J. Stat. Phys. 166 (2017) 680-713.
- An error term in the Central Limit Theorem for sums of discrete random variables (with Kasun Fernando) preprint.
- Multi-type branching processes with time-dependent branching rates (with Pratima Hebbar, Lenid Koralov, and Mark Perlman), preprint.

** Expositiory **

- Addendum to the paper Periodic points and dynamical spectra , by Viviane Baladi (with Mark Pollicott ) Ergodic Theory and Dynamical Systems 18 (1998) 293-301.
- 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. - Lectures on u-Gibbs states , Evanston, May 31-June 2, 2001.
- Sample path properties of random transformations , Kyoto, August 12, 2002,
- Introduction to averaging , Institut Henri Poincare, april-july 2005.
- 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.
- Hyperbolic billiards and statistical physics , (with Nikolai Chernov ), ICM, Madrid, August 2006.
- Diffusive motion and recurrence on generalized Galton board , (with Nikolai Chernov ), Phys. Rev. Lett. , 99 (2007) paper 030601.
- Fermi acceleration , Canadian Mathematical Society Winter Meeting. December 2006.
- Limit Theorems for Hyperbolic Systems, Beijing, August 2009.
- Piecewise smooth perturbations of integrable systems, International Congress of Mathematical Physics, Aalborg, Denmark, August 2012.
- Lectures on Bouncing Balls, Murcia, Spain, January 2013.
- Limit theorems for toral translations (with Bassam Fayad), Lousagne, June 2013.