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Positive topological entropy and $\ell_1$

David Kerr·Hanfeng Li
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Abstract

We characterize positive topological entropy for quasi-state space homeomorphisms induced from $C^*$-algebra automorphisms in terms of dynamically generated subspaces isomorphic to $\ell_1$. This geometric condition is also used to give a description of the topological Pinsker algebra. In particular we obtain a geometric characterization of positive entropy for topological dynamical systems, as well as an analogue for completely positive topological entropy of Glasner and Weiss's combinatorial characterization of completely positive Kolmogorov-Sinai entropy.

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David Kerr, Hanfeng Li. 2003-03-13. Positive topological entropy and $\ell_1$. https://arxiv.org/abs/math/0303161

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