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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2023

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Ergodic Theory and Dynamical Systems

ISSN

0143-3857

e-ISSN

1469-4417

Svazek periodika

43

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

27

Strana od-do

943-970

Kód UT WoS článku

000755540400001

EID výsledku v databázi Scopus

2-s2.0-85124961285