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.
Linear cocycles over hyperbolic systems and criteria of conformality
(with
B. Kalinin) pdf
Dimensional characteristics of invariant measures for circle diffeomorphisms
Ergodic Theory and Dynamical Systems, 29 (2009), no. 6, 1979-1992. pdf
On Anosov diffeomorphisms with asymptotically conformal periodic data
(with B. Kalinin)
Ergodic Theory and Dynamical Systems, 29 (2009), no. 1, 117-136. pdf
On the classification of resonance-free Anosov Zk actions
(with B. Kalinin)
Michigan Mathematical Journal,
vol. 55 (2007), no. 3, 651-670. pdf
Global rigidity for totally nonsymplectic Anosov Zk 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