Topological Methods in Nonlinear Analysis, Volume (48), No (2), Year (2016-1) , Pages (332-360)

Title : ( On the chaos game of iterated function systems )

Authors: Pablo Barrientos , Fateme Helen Ghane Ostadghassemi , Dominique Malicet , Ali Sarizadeh ,

Citation: BibTeX | EndNote

Abstract

Every quasi-attractor of an iterated function system (\rom{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 \rom{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 \rom{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 \rom{IFS}s

Keywords

, Iterated function system; well, fibred attractors; deterministic and probabilistic chaos game; forward and backward minimality
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@article{paperid:1058990,
author = {Pablo Barrientos and Ghane Ostadghassemi, Fateme Helen and Dominique Malicet and Ali Sarizadeh},
title = {On the chaos game of iterated function systems},
journal = {Topological Methods in Nonlinear Analysis},
year = {2016},
volume = {48},
number = {2},
month = {January},
issn = {1230-3429},
pages = {332--360},
numpages = {28},
keywords = {Iterated function system; well-fibred attractors; deterministic and probabilistic chaos game; forward and backward minimality},
}

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%0 Journal Article
%T On the chaos game of iterated function systems
%A Pablo Barrientos
%A Ghane Ostadghassemi, Fateme Helen
%A Dominique Malicet
%A Ali Sarizadeh
%J Topological Methods in Nonlinear Analysis
%@ 1230-3429
%D 2016

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