Diffeomorphisms of 2-manifolds with one-dimensional spaciously situated basic sets

Abstract

We consider orientation-preserving -diffeomorphisms of orientable surfaces of genus greater than one with a one-dimensional spaciously situated perfect attractor. We show that the topological classification of restrictions of diffeomorphisms to such basic sets can be reduced to that of pseudo-Anosov homeomorphisms with a distinguished set of saddles. In particular, we prove a result announced by Zhirov and Plykin, which gives a topological classification of the -diffeomorphisms of the surfaces under discussion under the additional assumption that the non-wandering set consists of a one-dimensional spaciously situated attractor and zero-dimensional sources.