Bi-Lyapunov Stable Homoclinic Classes for C1 Generic Flows

• 作者: Ru Song ZHENG
• 来源期刊: 数学学报（英文版）
• 年，卷（期）: 2021,（7）
• 页码范围: 1023-1040
• 页数: 18页
• 语种: 英文

摘要

We study bi-Lyapunov stable homoclinic classes for a C1 generic flow on a closed Rieman-nian 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.