Iterated Function Systems with the Weak Average Contraction Conditions. Issue 2 (3rd July 2019)

• Record Type: Journal Article
• Authors: Ehsani, A.; Ghane, F. H.
• Is Part Of: Journal of dynamical systems and geometric theories. Volume 17:Issue 2(2019)
• Page Start: 173
• Page End: 185
• Publication Date: 2019-07-03
• Subjects: 37B05 -- 37B10 -- 37A05 -- 37A25; Iterated function systems -- attractor -- weak average contraction condition -- chaos game; Differentiable dynamical systems -- Periodicals; Geometry -- Periodicals; Differentiable dynamical systems; Geometry; Periodicals; 515.39
• DOI: 10.1080/1726037X.2019.1651492
• Languages: English
• ISSNs: 1726-037X

Abstract

Abstract: 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.