Topologically Stable Chain Recurrence Classes for Diffeomorphisms

Abstract

Let f:M→M be a diffeomorphism of a finite dimension, smooth compact Riemannian manifold M. In this paper, we demonstrate that if a diffeomorphism f lies within the C1 interior of the set of all chain recurrence class-topologically stable diffeomorphisms, then the chain recurrence class is hyperbolic.

Keywords

• topologically stable
• chain recurrence class
• generic
• hyperbolic