Iterated Function Systems with the Weak Average Contraction Conditions

This paper concerns the chaos game of random iterated function systems. We consider a random iterated function system IFS( ) generated by a finite family of Lipschitz maps on a compact ball of ℝ n with the weak average contraction condition and show that it admits a quasi-attractor satisfying the de...

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Bibliographic Details
Published inJournal of dynamical systems and geometric theories Vol. 17; no. 2; pp. 173 - 185
Main Authors Ehsani, A., Ghane, F. H.
Format Journal Article
LanguageEnglish
Published Taylor & Francis 03.07.2019
Subjects
attractor
chaos game
Iterated function systems
weak average contraction condition
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Summary:This paper concerns the chaos game of random iterated function systems. We consider a random iterated function system IFS( ) generated by a finite family of Lipschitz maps on a compact ball of ℝ n with the weak average contraction condition and show that it admits a quasi-attractor satisfying the deterministic chaos game. In particular, these properties are preserved under small perturbations of the iterated function system IFS( ) with respect to the Lipschitz topology.
ISSN:1726-037X
2169-0057
DOI:10.1080/1726037X.2019.1651492