XXVI Workshop on Geometric Methods in Physics 1-7.07.2007

Alexey Zhirov

Pseudo-Anosov homeomorphisms and hyperbolic attractors of diffeomorphisms of surfaces

The problems of classification of hyperbolic attractors of surfaces diffeomorphisms, generalized pseugo-Anosov (GPA) homeomorhisms and conjugasy of automorphisms of fundamental groups of surfaces are closely related. In the talk the algorithmic approach to these problems will be discussed. It is based on combinatorial description of Markov partitions of some special kind (called band Markov partitions) and reconstruction of these Markov partitions. The method enables both to check topological conjugacy of two GPA-homeomorhisms or hyperbolic attractors and to enumerate them. The enumeration means to obtain the list of all GPA-homeomorhisms (hyperbolic attractors) with fixed structure of invariant foliations and given upper bound for topological entropy.