Devaney chaos of a set-valued map and its inverse limit

被引：1

作者：

Zhao, Yingcui ^{[1
]}

Wang, Lidong ^{[2
]}

Wang, Nan ^{[3
]}

机构：

[1] Dongguan Univ Technol, Sch Comp Sci & Technol, 1 Daxue Rd, Dongguan 523808, Guangdong, Peoples R China

[2] Zhuhai Coll Sci & Technol, Sch Stat & Data Sci, 8 Anji East Rd, Zhuhai 519041, Guangdong, Peoples R China

[3] Jilin Univ, Sch Math, 2699 Qianjin St, Chuangchun 130012, Jilin, Peoples R China

来源：

CHAOS SOLITONS & FRACTALS | 2023年 / 172卷

关键词：

Transitivity; Sensitivity; Devaney chaos; Set-valued maps; Generalized inverse limits; SPECIFICATION; PROPERTY;

D O I：

10.1016/j.chaos.2023.113454

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study relationships between a set-valued map and its inverse limit about the notion of periodic point set, transitivity, sensitivity and Devaney chaos. We show that periodic point set of a set-valued map is dense if and only if periodic point set of the inverse limit with the set-valued map is dense. Sensitivity of a set-valued map and its inverse limit are independent of each other. If the inverse limit with the set-valued map is chaotic in the sense of Devaney (respectively, transitive), then the set-valued map is chaotic in the sense of Devaney (respectively, transitive).

引用

页数：5

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