Asymptotic measure-expansiveness for generic diffeomorphisms

Abstract

In this paper, we will assume MM to be a compact smooth manifold and f:M→Mf:M\to M to be a diffeomorphism. We herein demonstrate that a C1{C}^{1} generic diffeomorphism ff is Axiom A and has no cycles if ff is asymptotic measure expansive. Additionally, for a C1{C}^{1} generic diffeomorphism ff, if a homoclinic class H(p,f)H\left(\hspace{0.08em}p,f) that contains a hyperbolic periodic point pp of ff is asymptotic measure-expansive, then H(p,f)H\left(\hspace{0.08em}p,f) is hyperbolic of ff.

Keywords

• expansive
• measure expansive
• asymptotic measure expansive
• generic
• axiom a
• homoclinic class
• hyperbolic
• 37c20
• 37d20