Dendrite-type attractors of IFSs formed by two injective functions

Dan Dumitru

Chaos, Solitons & Fractals, 2018, vol. 116, issue C, 433-438

Abstract: The aim of this paper is to study the dendrite-type attractors of an iterated function system formed by two injective functions. We consider (X, d) a complete metric space and S = (X, {f0, f1}) an iterated function system (IFS), where f0,f1:X⟶X are injective functions and A is the attractor of S. Moreover, we suppose that f0(A)∩f1(A)= {a} and {a}=π(0m1∞)=π(1n0∞) with m, n ≥ 1, where π is the canonical projection on the attractor. We compute the connected components of the sets A\{π(0∞)}, A\{π(1∞)}, A∖{π(0m1∞)=π(1n0∞)} and deduce there are infinitely-many (countably) non-homeomorphic dendrite-type attractors of iterated function systems formed by two injective functions.

Keywords: Attractor; Iterated function system; Dendrite; Connected component (search for similar items in EconPapers)
Date: 2018
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S096007791830986X
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:116:y:2018:i:c:p:433-438

DOI: 10.1016/j.chaos.2018.09.031

Access Statistics for this article

Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros

More articles in Chaos, Solitons & Fractals from Elsevier
Bibliographic data for series maintained by Thayer, Thomas R. ().