Open Access
Article
Adding machine maps and minimal sets for iterated function systems
*Mehdi Fatehi NiaCorresponding authorfatehiniam@yazd.ac.irDEPARTMENT OF MATHEMATICS, YAZD UNIVERSITY, P. O. BOX 89195-741Department of Mathematics, Yazd UniversityYazd, 89195-741, IranView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 27 Dec 2016
- Accepted:
- 29 Mar 2017
- Published Online:
- 02 Jan 2017
- Article type:
- Article
- Language:
- EN
- Article no.:
- 1726037X.2017.1324587
- Pages:
- 71–83
Abstract
In this paper, we focus attention on extending the topological conjugacy of adding machine maps and minimal systems to iterated function systems. We provide necessary and sufficient conditions for an iterated function system to be conjugated to an adding machine map. It is proved that every minimal iterated function system which has some non-periodic regular point is semi-conjugate to an adding machine map. Furthermore, we investigate the topological conjugacy of an infinite family of tent maps, as well as the restriction of a map to its ω—limit set with an iterated function system.
Keywords
Subject Classifications
37B5037C15
References
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