Entropy bounds through continuum theory

Morales, C.; San Martin, B.; Sirvent, V.

doi:10.1090/proc/15362

Entropy bounds through continuum theory
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by C. A. Morales, B. San Martin and V. F. Sirvent PDF

Proc. Amer. Math. Soc. 149 (2021), 1061-1075 Request permission

Abstract:

We will use continuum-theory to obtain an upper bound for the Kolmogorov-Sinai metric entropy. This bound (throughout called continuum-wise entropy) though different satisfies some properties resembling the metric entropy. Moreover, we prove that every ergodic measure with positive continuum-wise entropy is continuum-wise expansive.

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