The d-Shadowing Property and Average Shadowing Property for Iterated Function Systems
Joint Authors
Wang, Lidong
Jiang, Jie
Zhao, Yingcui
Source
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-04-29
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
In this paper, we introduce the definitions of d¯-shadowing property, d¯-shadowing property, topological ergodicity, and strong ergodicity of iterated function systems IFSf0,f1.
Then, we show the following: 1 if IFSf0,f1 has the d¯-shadowing property (respectively, d¯-shadowing property), then ℱk has the d¯-shadowing property (respectively, d¯-shadowing property) for any k∈Z+; 2 if ℱk has the d¯-shadowing property (respectively, d¯-shadowing property) for some k∈Z+, then IFSf0,f1 has the d¯-shadowing property (respectively, d¯-shadowing property); 3 if IFSf0,f1 has the d¯-shadowing property or d¯-shadowing property, and f0 or f1 is surjective, then IFSf0,f1 is chain mixing; 4 let f0,f1 be open maps.
For IFSf0,f1 with the d¯-shadowing property (respectively, d¯-shadowing property), if A⊂X is dense in X, and s is a minimal point of f0 or f1 for any s∈A, then IFSf0,f1 is strongly ergodic, and hence, ℱk is strongly ergodic; and 5 for IFSf0,f1 with the average shadowing property, if S⊂X is dense in X, and s is a quasi-weakly almost periodic point of f0 or f1 for any s∈S, then IFSf0,f1 is ergodic.
American Psychological Association (APA)
Jiang, Jie& Wang, Lidong& Zhao, Yingcui. 2020. The d-Shadowing Property and Average Shadowing Property for Iterated Function Systems. Complexity،Vol. 2020, no. 2020, pp.1-9.
https://search.emarefa.net/detail/BIM-1141916
Modern Language Association (MLA)
Jiang, Jie…[et al.]. The d-Shadowing Property and Average Shadowing Property for Iterated Function Systems. Complexity No. 2020 (2020), pp.1-9.
https://search.emarefa.net/detail/BIM-1141916
American Medical Association (AMA)
Jiang, Jie& Wang, Lidong& Zhao, Yingcui. The d-Shadowing Property and Average Shadowing Property for Iterated Function Systems. Complexity. 2020. Vol. 2020, no. 2020, pp.1-9.
https://search.emarefa.net/detail/BIM-1141916
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1141916