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Bi-Lyapunov Stable Homoclinic Classes for C1 Generic Flows
Acta Mathematica Sinica, English Series ( IF 0.8 ) Pub Date : 2021-07-15 , DOI: 10.1007/s10114-021-0420-8
Ru Song Zheng 1
Affiliation  

We study bi-Lyapunov stable homoclinic classes for a C1 generic flow on a closed Riemannian manifold and prove that such a homoclinic class contains no singularity. This enables a parallel study of bi-Lyapunov stable dynamics for flows and for diffeomorphisms. For example, we can then show that a bi-Lyapunov stable homoclinic class for a C1 generic flow is hyperbolic if and only if all periodic orbits in the class have the same stable index.



中文翻译:

C1 泛型流的双李雅普诺夫稳定同宿类

我们研究了闭黎曼流形上C 1泛型流的双李雅普诺夫稳定同宿类,并证明这样的同宿类不包含奇点。这使得能够并行研究流动和微分同胚的双李雅普诺夫稳定动力学。例如,我们可以证明C 1泛型流的双李雅普诺夫稳定同宿类是双曲线的,当且仅当该类中的所有周期轨道都具有相同的稳定指数。

更新日期:2021-07-27
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