In Middle Volga Mathematical Society

On topological classification of grad-like diffeomorphisms on surfaces by means of three-color graph

S. H. Kapkaeva

Mordovian State University, Saransk

Abstract: The paper is devoted to finding of necessary and sufficient conditions for topological conjugacy of gradient-like diffeomorphisms on surfaces whose non-wandering set consists of fixed points. It is shown that three-color graph (deneralising the similar concept introduced in paper [4]) associated with given diffeomorphism is complete topological invariant of diffeomorphism from considered class.

Keywords: Morse-Smale diffeomorphisms, gradient-like diffeomorphisms, topological conjugate diffeomorphisms, three-color graph.

UDC: 517.938.5