Lyapunov stable homoclinic classes for smooth vector fields

Abstract

In this paper, we show that for generic C1, if a flow Xt has the shadowing property on a bi-Lyapunov stable homoclinic class, then it does not contain any singularity and it is hyperbolic.

Keywords

• homoclinic class
• lyapunov stable
• shadowing
• generic
• hyperbolic
• 37c50
• 37c10
• 37c20
• 37c29
• 37d05