Robinson's chaos in set-valued discrete systems

Heriberto Román-Flores; Y. Chalco-Cano

doi:10.1016/j.chaos.2004.11.006

Robinson's chaos in set-valued discrete systems

Heriberto Román-Flores
, Y. Chalco-Cano

Department of Mathematics

Universidad de Tarapacá

Research output: Contribution to journal › Article › peer-review

62 Scopus citations

Abstract

Let (X, d) be a compact metric space and f: X → X a continuous function. If we consider the space (K(X),H) of all non-empty compact subsets of X endowed with the Hausdorff metric induced by d and f̄:K(X)→K(X), f̄(A)={f(a)/a∈A}, then the aim of this work is to show that Robinson's chaos in f̄ implies Robinson's chaos in f. Also, we give an example showing that R-chaos in f does not implies R-chaos in f̄.

Original language	English
Pages (from-to)	33-42
Number of pages	10
Journal	Chaos, Solitons and Fractals
Volume	25
Issue number	1
DOIs	https://doi.org/10.1016/j.chaos.2004.11.006
State	Published - Jul 2005

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title = "Robinson's chaos in set-valued discrete systems",

abstract = "Let (X, d) be a compact metric space and f: X → X a continuous function. If we consider the space (K(X),H) of all non-empty compact subsets of X endowed with the Hausdorff metric induced by d and {\=f}:K(X)→K(X), {\=f}(A)=\{f(a)/a∈A\}, then the aim of this work is to show that Robinson's chaos in {\=f} implies Robinson's chaos in f. Also, we give an example showing that R-chaos in f does not implies R-chaos in {\=f}.",

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AU - Chalco-Cano, Y.

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AB - Let (X, d) be a compact metric space and f: X → X a continuous function. If we consider the space (K(X),H) of all non-empty compact subsets of X endowed with the Hausdorff metric induced by d and f̄:K(X)→K(X), f̄(A)={f(a)/a∈A}, then the aim of this work is to show that Robinson's chaos in f̄ implies Robinson's chaos in f. Also, we give an example showing that R-chaos in f does not implies R-chaos in f̄.

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Robinson's chaos in set-valued discrete systems

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