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- Publisher
- Springer Journals
- Copyright
- Copyright © Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2021
- ISSN
- 0126-6705
- eISSN
- 2180-4206
- DOI
- 10.1007/s40840-021-01184-x
- Publisher site
- See Article on Publisher Site
Abstract
In this paper, we explore the asymptotic average shadowing property of iterated function systems. We show that for an iterated function system IFS(F)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$(\mathscr {F})$$\end{document} such that one of F\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\mathscr {F}$$\end{document} is surjective, the pseudo-orbital specification implies the asymptotic average shadowing, and by this result, we obtain that the ergodic shadowing implies the asymptotic average shadowing. Moreover, we also prove that the asymptotic average shadowing implies the average shadowing. Furthermore, we give criteria for an iterated function system that does not have the asymptotic average shadowing property.
Journal
Bulletin of the Malaysian Mathematical Sciences Society – Springer Journals
Published: Jan 1, 2022
Keywords: Ergodic shadowing; Average shadowing; Iterated function system; Primary: 37C50; Secondary 37C15