Some papers and preprints.

Research

1. Multifractal properties of sets of zeroes of Brownian path (with Vadim Sidorov) Fundamenta Mathematicae 147 (1995) 157-171, dvi , pdf .
2. Bounded orbits of Anosov flows. Duke Math. J. 87 (1997) 87-114, dvi , pdf.
3. Entropy of coupled map lattices. J. Stat. Phys. 86 (1997) 377-389, dvi , pdf .
4. Decay of Correlations
   • On decay of correlations in Anosov flows , Ann. of Math. 147 (1998) 357-390, dvi , pdf .
   • Prevalence of rapid mixing:
     Part I: Ergodic Theory and Dynamical Systems 18 (1998) 1097-1114, dvi , pdf .
     Part II: Ergodic Theory and Dynamical Systems 20 (2000) 1045-1059. dvi , pdf .
   • On dynamics of mostly contracting diffeomorphisms, Comm. in Math. Physics , 213 (2000) 181-201. dvi , pdf .
   • On mixing properties of compact group extensions of hyperbolic systems, Israel J. Math. , 130 (2002) 157-205. dvi , pdf .
5. Every compact manifold carries a complitely hyperbolic diffeomorphism, (with Yakov Pesin ), Ergodic Theory and Dynamical Systems , 22 (2002) 409-437. dvi , pdf .
6. Stable accessibility is C1 dense (with Amie Wilkinson ), Asterisque 287 (2003), 33-60. dvi , pdf .
7. Limit Theorems for partially hyperbolic systems, Transactions of the AMS 356 (2004) 1637-1689. dvi , pdf .
8. Perturbation Theory for Invariant measures
   • On differentiability of SRB states for partially hyperbolic systems, Invent. Math. 155 (2004) 389--449. dvi , pdf .
   • Averaging and Invariant measures , Moscow Math. J. 5 (2005) 537-576. dvi , pdf .
   • Prelude to a kiss, dvi , pdf , Modern dynamical systems (edited by Misha Brin , Boris Hasselblatt and Yakov Pesin ), Cambridge Unversity Press, 2004, 313-324.
9. Dynamics of Stochastic Flows (with Vadim Kaloshin and Leonid Koralov)
   • Sample path properties of stochastic flows, Ann. Prob. , 32 (2004) 1-27. dvi , pdf .
   • Hausdorff Dimension in Stochastic Dispersion, J. Stat. Phys. , 108 (2002) 943-971. dvi , pdf .
   • A limit shape theorem for periodic stochastic dispersion, CPAM , 57 (2004) 1127-1158. dvi , pdf .
10. Livsic theory for compact group extensions of hyperbolic systems, Moscow Math. J. 5 (2005) 55-66. dvi , pdf .
11. On simultaneous linearization of diffeomorphisms of the sphere (with Raphael Krikorian ), Duke Math. J. , 136 (2007) 475-505. dvi , pdf .
12. Evolution of adiabatic invariants in stochastic averaging, Stochastics and Dynamics 4 (2004) 265-275. dvi , pdf .
13. Brownian Brownian Motion-1 (with Nikolai Chernov ), to appear in Memoirs AMS, dvi , pdf .
14. Avergaging of Hamiltonian flows with an ergodic component, (with Leonid Koralov ), to appear in Ann. Prob. , dvi , pdf .
15. Dynamics of Lorentz gas (with Domokos Szasz and Tamas Varju)
    • Recurrence properties of Lorentz gas Duke Math. J. 142 (2008) 241-281, dvi , pdf .
    • Limit Theorems for Locally Perturbed Lorentz processes, preprint dvi , pdf .
16. Random walks in Markovian enviroment (with Carlangelo Liverani and Gerhard Keller), to appear in Ann. Prob. , dvi , pdf .
17. Fermi acceleration
    • Bouncing balls in non-linear potentials, to appeaer in Discrete and Continuous Dynamical Systems - A , dvi , pdf .
    • Galton board: Limit Theorems and Recurrence (with Nikolai Chernov ), preprint pdf , dvi .
    • Motion in a random force field (with Leonid Koralov ), preprint dvi , pdf .
    • Unbounded orbits for semicircular outer billiard (with Bassam Fayad), preprint, dvi , pdf .
18. Particle's drift in self-similar billiards (with Nikolai Chernov ), Ergodic Theory and Dynamical Systems 28 (2008) 389-403. dvi , pdf .
19. Repulsion from Resonances, Preliminary version, dvi , pdf .

Expositiory

1. Addendum to Periodic points and dynamical spectra by Viviane Baladi (with Mark Pollicott ) Ergodic Theory and Dynamical Systems 18 (1998) 293-301, dvi , pdf .
2. Addendum to 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, dvi , pdf .
3. Lectures on u-Gibbs states, Evanston, May 31-June 2, 2001, dvi , pdf .
4. Sample path properties of random transformations, Kyoto, August 12, 2002, dvi , pdf .
5. Introduction to averaging, Institut Henri Poincare, april-july 2005, dvi , pdf .
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. dvi , pdf
7. Hyperbolic billiards and statistical physics (with Nikolai Chernov ), dvi , pdf . ICM, Madrid, August 2006.
8. Diffusive motion and recurrence on generalized Galton board (with Nikolai Chernov ), Phys. Rev. Lett. , 99 (2007) paper 030601, dvi , pdf .
9. Fermi acceleration, Canadian Mathematical Society Winter Meeting, December 2006 dvi , pdf .