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

Cordeiro, Welington; Pacífico, Maria

doi:10.1090/proc/13168

Continuum-wise expansiveness and specification for set-valued functions and topological entropy
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by Welington Cordeiro and Maria José Pacífico PDF

Proc. Amer. Math. Soc. 144 (2016), 4261-4271 Request permission

Abstract:

We define the concept of continuum-wise expansiveness for set-valued functions. We prove that for a compact metric space $X$ with positive topological dimension, if a set-valued function is $cw$-expansive, then its topological entropy is positive. We also introduce the notion of point-wise specification property for set-valued functions and prove that set-valued functions with this property have positive entropy.

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