Topological entropy for induced hyperspace maps

Jose S. Cánovas Peña and Gabriel Soler López

Chaos, Solitons & Fractals, 2006, vol. 28, issue 4, 979-982

Abstract: Let (X,d) be a compact metric space and let f:X→X be continuous. Let K(X) be the family of compact subsets of X endowed with the Hausdorff metric and define the extension f¯:K(X)→K(X) by f¯(K)=f(K) for any K∈K(X). We prove that the topological entropy of f¯ is greater or equal than the topological entropy of f, and this inequality can be strict. On the other hand, we prove that the topological entropy of f is positive if and only if the topological entropy of f¯ is also positive.

Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:28:y:2006:i:4:p:979-982

DOI: 10.1016/j.chaos.2005.08.173

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