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Diffeomorphisms of 2-manifolds with one-dimensional spaciously situated basic sets
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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.
Title: Diffeomorphisms of 2-manifolds with one-dimensional spaciously situated basic sets
Description:
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.
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