Classification of One-Dimensional Attractors of Diffeomorphisms of Surfaces by Means of Pseudo-Anosov Homeomorphisms

Abstract

Axiom A diffeomorphisms of closed 2-manifold of genus \(p \geqslant 2\) whose nonwandering set contains a perfect spaciously situated one-dimensional attractor are considered. It is shown that such diffeomorphisms are topologically semiconjugate to a pseudo-Anosov homeomorphism with the same induced automorphism of fundamental group. The main result of this paper is as follows. Two diffeomorphisms from the given class are topologically conjugate on perfect spaciously situated attractors if and only if the corresponding homotopic pseudo-Anosov homeomorphisms are topologically conjugate by means of a homeomorphism that maps a certain subset of one pseudo-Anosov homeomorphism onto a subset of the other.