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

S. H. Kapkaeva1

Annotation 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 Morse-Smale gradient-like diffeomorphism topological conjugacy, attractor, repeller

1Student, Mordovian State University after N.P. Ogarev, Saransk; kapkaevasvetlana@yandex.ru.

Citation: S. H. Kapkaeva, "[On the topological conjugacy of gradient-like diffeomorphisms of surfaces with one-dimensional invariant sets]", Zhurnal Srednevolzhskogo matematicheskogo obshchestva,16:1 (2014) 76–82 (In Russian)