Ergodic theorems for actions of Markov groups.
Markov partitions for pseudo-Anosov diffeomorphisms of 2-dimensional surfaces.
Main publications:
A. I. Bufetov, A. V. Klimenko, M. I. Khristoforov, “Cesàro convergence of spherical averages for Markov groups and semigroups”, Russian Math. Surveys, 66:3 (2011), 633–634
A. V. Klimenko, “The number of classes of Markov partitions for a hyperbolic automorphism of a 2-torus”, Sb. Math., 200:8 (2009), 1247–1259