Research Interests

My research is in the area of  Dynamical Systems and Ergodic Theory.

I am primarily interested in smooth dynamics and rigidity of hyperbolic and partially hyperbolic systems,
as well as of higher rank abelian actions. In particular, I considered such systems with higher dimensional
invariant foliations and studied the role of pinching and conformality conditions.

I have also worked in dimension theory of dynamical systems. The main objects of study in this area are
dimensional properties of natural invariant sets and measures.

Publications and Preprints

On Anosov diffeomorphisms with asymptotically conformal periodic data
(with B. Kalinin)   To appear in Ergodic Theory and Dynamical Systems.     pdf

On the classification of resonance-free Anosov Z^k actions
(with B. Kalinin)   Michigan Mathematical Journal, vol. 55 (2007), no. 3, 651--670.     pdf

Global rigidity for totally nonsymplectic Anosov Z^k actions
(with B. Kalinin)   Geometry and Topology, vol. 10 (2006), 929-954.     pdf

On the regularity of integrable conformal structures invariant under Anosov systems
(with R. de la Llave)   Discrete and Continuous Dynamical Systems, vol. 12 (2005), no. 3, 377-385.     pdf

On local and global rigidity of quasiconformal Anosov diffeomorphisms
(with B. Kalinin)   Journal of the Institute of Mathematics of Jussieu, 2 (2003), no. 4, 567-582.     pdf

On uniformly quasiconformal Anosov systems
Mathematical Research Letters, vol. 12 (2005), no. 3, 425-441.     pdf

On pointwise dimension of non-hyperbolic measures
(with B. Kalinin)   Ergodic Theory and Dynamical Systems, 22 (2002), no. 6, 1783-1801.     pdf

Multifractal analysis of conformal Axiom A flows
(with Ya. Pesin)   Communications in Mathematical Physics (2001), 216, 277-312.     pdf