In Middle Volga Mathematical Society

On topology of ambient manifold for Morse-Smale diffeomorphisms.

E. Ya. Gurevich

N. I. Lobachevski State University of Nizhni Novgorod

Abstract: In this article is considered the class $G(M^3)$ of orientation preserving Morse-Smale diffeomorphisms on connected closed orientable 3-manifolds such that for any $f\in G(M^3)$ the set of unstable separatrices is one-dimensional and does not contain any heteroclinic intersection. It is proved that for any $f\in G(M^3)$ its' ambient manifold $M^3$ is diffeomorphic to 3-sphere.

Keywords: Morse-Smale dynamical systems, topology of the ambient manifold.

UDC: 517.938

Received: 02.12.2011