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Uniformly positive entropy of induced transformations
Published online by Cambridge University Press: 28 December 2020
Abstract
Let
$(X,T)$
be a topological dynamical system consisting of a compact metric space X and a continuous surjective map
$T : X \to X$
. By using local entropy theory, we prove that
$(X,T)$
has uniformly positive entropy if and only if so does the induced system
$({\mathcal {M}}(X),\widetilde {T})$
on the space of Borel probability measures endowed with the weak* topology. This result can be seen as a version for the notion of uniformly positive entropy of the corresponding result for topological entropy due to Glasner and Weiss.
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- Original Article
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- Copyright
- © The Author(s), 2020. Published by Cambridge University Press
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