Topological version of generalized (infinite) iterated function systems. (February 2015)

• Record Type: Journal Article
• Authors: Dumitru, Dan; Ioana, Loredana; Sfetcu, Răzvan-Cornel; Strobin, Filip
• Is Part Of: Chaos, solitons and fractals. Volume 71(2015)
• Page Start: 78
• Page End: 90
• Publication Date: 2015-02
• Subjects: Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2014.12.005
• Languages: English
• ISSNs: 0960-0779

Abstract

Abstract: Our paper is an attempt to unify various generalizations of IFSs which appeared in the literature in the last years. We extend the notion of a generalized iterated function system (introduced by Miculescu and Mihail in 2008) to the topological and (possible) infinite case. Then we prove that many classical results (for example the existence of a unique attractor) hold for this extended case.