In Middle Volga Mathematical Society

On the topological conjugacy of gradient-like diffeomorphisms of surfaces with one-dimensional invariant sets

S. H. Kapkaeva

Ogarev Mordovia State University

Abstract: In the paper we found conditions for the topological conjugacy of gradient-like 2-diffeomorphisms whose nonwandering set belongs to the invariant finite union of disjoint simple closed curves. The interrelation between the dynamics of diffeomorphisms and the topology of the ambient manifold is established. For a meaningful subclass of such systems their topological classification obtained

Keywords: Morse-Smale gradient-like diffeomorphism topological conjugacy, attractor, repeller.

UDC: 517.938.5

Received: 18.07.2014