On mixing property in set-valued discrete systems

Rongbao Gu and Wenjing Guo

Chaos, Solitons & Fractals, 2006, vol. 28, issue 3, 747-754

Abstract: Let (X,d) be a compact metric space and f:X→X be a continuous map. Let (K(X),H) be the space of all non-empty compact subsets of X endowed with the Hausdorff metric induced by d and f¯:K(X)→K(X) be the map defined by f¯(A):{f(a):a∈A}. In this paper we investigate the relationships between the mixing property of (K(X),f¯) and the mixing property of (X,f). In addition, we discuss specification for the set-valued discrete dynamical system (K(X),f¯).

Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:28:y:2006:i:3:p:747-754

DOI: 10.1016/j.chaos.2005.04.004

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