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

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985556%3A_____%2F23%3A00561667" target="_blank" >RIV/67985556:_____/23:00561667 - isvavai.cz</a>
Result on the web
<a href="https://www.cambridge.org/core/journals/ergodic-theory-and-dynamical-systems/article/abs/on-bar-d-approachability-entropy-density-and-mathscr-b-free-shifts/F5D747D79D4C4ED5282AED0F63DDC8CA" target="_blank" >https://www.cambridge.org/core/journals/ergodic-theory-and-dynamical-systems/article/abs/on-bar-d-approachability-entropy-density-and-mathscr-b-free-shifts/F5D747D79D4C4ED5282AED0F63DDC8CA</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1017/etds.2021.167" target="_blank" >10.1017/etds.2021.167</a>

Result language
angličtina
Original language name
On d-approachability, entropy density and B-free shifts
Original language description
We study approximation schemes for shift spaces over a finite alphabet using (pseudo)metrics connected to Ornstein's (d) over bar metric. This leads to a class of shift spaces we call (d) over bar -approachable. A shift space is (d) over bar -approachable when its canonical sequence of Markov approximations converges to it also in the (d) over bar sense. We give a topological characterization of chain-mixing (d) over bar -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 mu of such a shift space is the weak* limit of a sequence mu(n) of ergodic measures with the corresponding sequence of entropies h(mu) converging to h(mu) . We prove ergodic measures are entropy-dense for every shift space that can be approximated in the (d) over bar pseudometric by a sequence of transitive sofic shifts. This criterion can be applied to many examples that were beyond the reach of previously known techniques including hereditary B-free shifts and some minimal or proximal systems. The class of symbolic dynamical systems covered by our results includes also shift spaces where entropy density was established previously using the (almost) specification property.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10102 - Applied mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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