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arXiv · 1510.07615

Continuum-wise expansiveness and specification for set-valued functions and topological entropy

Welington Cordeiro·Maria José Pacífico
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Abstract

We define the concept of continuum wise expansive for set-valued functions and prove that if a compact metric space admit a set-valued $cw$-expansive function then the topological entropy of $X$ is positive.} We also introduce the notion of pointwise specification property for set-valued functions and prove that set-valued functions with this property has positive entropy.

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Welington Cordeiro, Maria José Pacífico. 2015-10-26. Continuum-wise expansiveness and specification for set-valued functions and topological entropy. https://arxiv.org/abs/1510.07615

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