Measure-Expansive Homoclinic Classes for C1 Generic Flows

Mathematics

Manseob Lee¹ 

[1] Department of Mathematics, Mokwon University, Daejeon 302-729, Korea;

关键词: expansive;    measure-expansive;    homoclinic class;    generic;    hyperbolic;   

DOI  :  10.3390/math8081232

来源: DOAJ

【 摘 要 】

In this paper, we prove that for a generically $C^1$ vector field X of a compact smooth manifold M, if a homoclinic class $H(\gamma ,X)$ which contains a hyperbolic closed orbit $\gamma$ is measure expansive for X then $H(\gamma ,X)$ is hyperbolic.

【 授权许可】

Unknown