Preservation of shadowing in discrete dynamical systems

Chris Good; Joel Mitchell; Joe Thomas

doi:10.1016/j.jmaa.2019.123767

Preservation of shadowing in discrete dynamical systems

Chris Good, Joel Mitchell, Joe Thomas

Mathematics

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

184 Downloads (Pure)

Abstract

We look at the preservation of various notions of shadowing in discrete dynamical systems under inverse limits, products, factor maps and the induced maps for symmetric products and hyperspaces. The shadowing properties we consider are the following: shadowing, h-shadowing, eventual shadowing, orbital shadowing, strong orbital shadowing, the first and second weak shadowing properties, limit shadowing, s-limit shadowing, orbital limit shadowing and inverse shadowing.

Original language	English
Article number	123767
Pages (from-to)	1-39
Number of pages	39
Journal	Journal of Mathematical Analysis and Applications
Volume	485
Issue number	1
Early online date	13 Dec 2019
DOIs	https://doi.org/10.1016/j.jmaa.2019.123767
Publication status	Published - 1 May 2020

Keywords

factor map
hyperspace
inverse limit
product space
semi-conjugacy
shadowing

ASJC Scopus subject areas

General Mathematics

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Good_et_al_Preservation_of_shadowing_in_discrete_dynamical_systems_Journal_of_Mathematical_Analysis_and_Applications_2019Accepted author manuscript, 444 KBLicence: Creative Commons: Attribution-NonCommercial-NoDerivs (CC BY-NC-ND)

https://www.sciencedirect.com/science/article/pii/S0022247X19310352Licence: None: All rights reserved

Cite this

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AB - We look at the preservation of various notions of shadowing in discrete dynamical systems under inverse limits, products, factor maps and the induced maps for symmetric products and hyperspaces. The shadowing properties we consider are the following: shadowing, h-shadowing, eventual shadowing, orbital shadowing, strong orbital shadowing, the first and second weak shadowing properties, limit shadowing, s-limit shadowing, orbital limit shadowing and inverse shadowing.

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Preservation of shadowing in discrete dynamical systems

Abstract

Keywords

ASJC Scopus subject areas

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