Bi-Lyapunov St able Homoclinic Classes for C^(1)Generic Flows  

作　　者：Ru Song ZHENG 

机构地区：[1]School of Innovation and Entrepreneur ship,Southern University of Science and Technology,Shenzhen 518055,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2021年第7期1023-1040,共18页数学学报（英文版）

摘　　要：We study bi-Lyapunov stable homoclinic classes for a C^(1)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 tha t a bi-Lyapunov st able 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.

关 键 词：Bi-Lyapunov stable homoclinic class SINGULARITY dominated splitting linear cocycle 

分 类 号：O175[理学—数学]