The Structural Stability of Maps with Heteroclinic Repellers

被引：6

作者：

Chen, Yuanlong ^{[1
]}

Li, Liangliang ^{[2
]}

Wu, Xiaoying ^{[1
]}

Wang, Feng ^{[1
]}

机构：

[1] Guangdong Univ Finance, Sch Financial Math & Stat, Guangzhou 510521, Peoples R China

[2] Sun Yat Sen Univ, Sino French Inst Nucl Engn & Technol, Guangzhou 510275, Guangdong, Peoples R China

来源：

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2020年 / 30卷 / 14期

基金：

中国国家自然科学基金;

关键词：

Heteroclinic repeller; structural stability; chaos; positive topological entropy; SNAP-BACK REPELLERS; BOUNDARY-CONDITION; CHAOTIC VIBRATION; PERTURBATIONS; PERSISTENCE; VAN;

D O I：

10.1142/S0218127420502077

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This note is concerned with the effect of small C-1 perturbations on a discrete dynamical system (X,f), which has heteroclinic repellers. The question to be addressed is whether such perturbed system (X,g) has heteroclinic repellers. It will be shown that if parallel to f - g parallel to(C1) is small enough, (X,g) has heteroclinic repellers, which implies that it is chaotic in the sense of Devaney. In addition, if X = R-n and (X,f) has regular nondegenerate heteroclinic repellers, then (X,g) has regular nondegenerate heteroclinic repellers, where g is a small Lipschitz perturbation of f. Three examples are presented to validate the theoretical conclusions.

引用

页数：10

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