Banach空间中正则非退化异宿环的Lipschitz扰动  

The Lipschitz Perturbations of Regular Nondegenrate Heteroclinic Cycles in Banach Spaces

作　　者：陈员龙 骆世广 Yuan Long CHEN;Shi Guang LUO(School of Financial Mathermatics ahd Statistics,Guangdong University of Finance,Guangzhou 510521,P.R.China)

机构地区：[1]广东金融学院金融数学与统计学院,广州510521

出　　处：《数学学报（中文版）》2021年第3期485-492,共8页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金(11671410);广东省自然科学基金(2017A030313037,2018A0303130120);广东省普通高校自然科学重点项目(2019KZDXM036)资助项目。

摘　　要：本文研究Banach空间上离散动力系统的Lipschitz扰动.设f,g是Banach空间(X,||·||)上的连续自映射.如果f具有正则非退化返回排斥子或正则非退化异宿环且g是f的Lipschitz小扰动,则g也有正则非退化返回排斥子或正则非退化异宿环.另外,本文还证明完备度量空间中正则非退化异宿环蕴含正则非退化返回排斥子.This note is concerned with the effect of small Lipschitz perturbations of a discrete dynamical system in Banach spaces.Let f,g be continuous map from a Banach space X into itself.If f has regular nondegenrate snap-back repellers or heteroclinic cycles and g is a small Lipschitz perturbations of f,then g has regular nondegenrate snap-back repellers or heteroclinic cycles.In addition,the regular nondegenrate heteroclinic cycles implying the snap-back repellers is studied in complete metric spaces.

关 键 词：离散动力系统 Lipschitz扰动 混沌 异宿环 结构稳定性 

分 类 号：O19[理学—数学]