Adding machine maps and minimal sets for iterated function systems. Issue 1 (2nd January 2017)

• Record Type: Journal Article
• Authors: Nia, Mehdi Fatehi
• Is Part Of: Journal of dynamical systems and geometric theories. Volume 15:Issue 1(2017)
• Page Start: 71
• Page End: 83
• Publication Date: 2017-01-02
• Subjects: 37B50 -- 37C15; Adding machine map -- Iterated function systems -- Minimal set -- Regularly recurrent -- Topological conjugacy; Differentiable dynamical systems -- Periodicals; Geometry -- Periodicals; Differentiable dynamical systems; Geometry; Periodicals; 515.39
• DOI: 10.1080/1726037X.2017.1324587
• Languages: English
• ISSNs: 1726-037X

Abstract

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.