Article Dans Une Revue Ergodic Theory and Dynamical Systems Année : 2022

On d-bar-approachability, entropy density and B-free shifts

Résumé

We study approximation schemes for shift spaces over a finite alphabet using (pseudo)metrics connected to Ornstein's d metric. This leads to a class of shift spaces we call d-approachable. A shift space d-approachable when its canonical sequence of Markov approximations converges to it also in the d sense. We give a topological characterisation of chain mixing d-approachable shift spaces. As an application we provide a new criterion for entropy density of ergodic measures. Entropy-density of a shift space means that every invariant measure µ of such a shift space is the weak * limit of a sequence µn of ergodic measures with the corresponding sequence of entropies h(µn) converging to h(µ). We prove ergodic measures are entropy-dense for every shift space that can be approximated in the d

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hal-03919578 , version 1 (03-01-2023)

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Jakub Konieczny, Michal Kupsa, Dominik Kwietniak. On d-bar-approachability, entropy density and B-free shifts. Ergodic Theory and Dynamical Systems, 2022, pp.1-28. ⟨10.1017/etds.2021.167⟩. ⟨hal-03919578⟩
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