Measure-Expansive Homoclinic Classes for <i>C</i>¹ Generic Flows

Abstract

In this paper, we prove that for a generically C1 vector field X of a compact smooth manifold M, if a homoclinic class H(γ,X) which contains a hyperbolic closed orbit γ is measure expansive for X then H(γ,X) is hyperbolic.

Keywords

• expansive
• measure-expansive
• homoclinic class
• generic
• hyperbolic