Open Access
2017 On the chaos game of iterated function systems
Pablo G. Barrientos, Fatemeh H. Ghane, Dominique Malicet, Aliasghar Sarizadeh
Topol. Methods Nonlinear Anal. 49(1): 105-132 (2017). DOI: 10.12775/TMNA.2016.064


Every quasi-attractor of an iterated function system (IFS) of continuous functions on a first-countable Hausdorff topological space is renderable by the probabilistic chaos game. By contrast, we prove that the backward minimality is a necessary condition to get the deterministic chaos game. As a consequence, we obtain that an IFS of homeomorphisms of the circle is renderable by the deterministic chaos game if and only if it is forward and backward minimal. This result provides examples of attractors (a forward but no backward minimal IFS on the circle) that are not renderable by the deterministic chaos game. We also prove that every well-fibred quasi-attractor is renderable by the deterministic chaos game as well as quasi-attractors of both, symmetric and non-expansive IFSs.


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Pablo G. Barrientos. Fatemeh H. Ghane. Dominique Malicet. Aliasghar Sarizadeh. "On the chaos game of iterated function systems." Topol. Methods Nonlinear Anal. 49 (1) 105 - 132, 2017.


Published: 2017
First available in Project Euclid: 11 April 2017

zbMATH: 1373.37054
MathSciNet: MR3635639
Digital Object Identifier: 10.12775/TMNA.2016.064

Rights: Copyright © 2017 Juliusz P. Schauder Centre for Nonlinear Studies

Vol.49 • No. 1 • 2017
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