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Journal of Dynamical Systems and Geometric Theories

(Since 2002)
Open Access ·Peer-reviewed·ISSN (Online): 2169-0057·ISSN (Print): 1726-037X

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Half-Yearly Journal: Publishes research on dynamical systems and geometry, including Random Dynamical Systems, hyperbolic behaviour, complex geometry and Ergodic theory.

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Journal of Dynamical Systems and Geometric Theories
Open Access Research Article

Chain Mixing and Chain Transitive Iterated Function Systems

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pp. 211–221Vol. 18Issue 2July 2020DOI: 10.1080/1726037X.2020.1856338XML
Received:
11 May 2020
Accepted:
11 Aug 2020
Published Online:
07 Jan 2021
Article type:
Research Article
Language:
EN
Article no.:
1726037X.2020.1856338
Pages:
211–221

Abstract

This paper considers some properties in topological dynamical systems in iterated function systems. First, we will introduce chain mixing and chain transitive iterated function systems then some results and an example is presented to compare with these notions in discrete dynamical systems. As our main result, using adding machine maps and topological conjugacy we show that chain mixing, chain transitive and chain recurrence properties in iterated function systems are equivalent.

Keywords

Adding machine mapsChain mixingChain recurrentChain transitiveIterated function sy.stems

Subject Classifications

37C5037C15

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