Bi-Lyapunov Stable Homoclinic Classes for C1 Generic Flows

被引：0

作者：

Zheng, Ru Song ^{[1
]}

机构：

[1] Southern Univ Sci & Technol, Sch Innovat & Entrepreneurship, Shenzhen 518055, Peoples R China

来源：

ACTA MATHEMATICA SINICA-ENGLISH SERIES | 2021年 / 37卷 / 07期

关键词：

Bi-Lyapunov stable; homoclinic class; singularity; dominated splitting; linear cocycle; PERIODIC-ORBITS; SETS; HYPERBOLICITY;

D O I：

10.1007/s10114-021-0420-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study bi-Lyapunov stable homoclinic classes for a C-1 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 C-1 generic flow is hyperbolic if and only if all periodic orbits in the class have the same stable index.

引用

页码：1023 / 1040

页数：18

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