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Dendrite-type attractors of IFSs formed by two injective functions

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  • Dumitru, Dan

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.

Suggested Citation

  • Dumitru, Dan, 2018. "Dendrite-type attractors of IFSs formed by two injective functions," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 433-438.
    • Handle: RePEc:eee:chsofr:v:116:y:2018:i:c:p:433-438
    DOI: 10.1016/j.chaos.2018.09.031
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