On entropy of dynamical systems with almost specification

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17610%2F16%3AA1701EL0" target="_blank" >RIV/61988987:17610/16:A1701EL0 - isvavai.cz</a>

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

On entropy of dynamical systems with almost specification

Popis výsledku v původním jazyce

We construct a family of shift spaces with almost specification and multiple measures of maximal entropy. This answers a question from Climenhaga and Thompson [emph{Israel J. Math.} textbf{192} (2012), no. 2, 785--817]. Elaborating on our examples we prove that sufficient conditions for every shift factor of a shift space to be intrinsically ergodic given by Climenhaga and Thompson are in some sense best possible, moreover, the weak specification property neither implies intrinsic ergodicity, nor follows from almost specification. We also construct a dynamical system with the weak specification property, which does not have the almost specification property. We prove that the minimal points are dense in the support of any invariant measure of a system with the almost specification property. Furthermore, if a system with almost specification has an invariant measure with non-trivial support, then it also has uniform positive entropy over the support of any invariant measure and can not be minimal.

Název v anglickém jazyce

On entropy of dynamical systems with almost specification

Popis výsledku anglicky

We construct a family of shift spaces with almost specification and multiple measures of maximal entropy. This answers a question from Climenhaga and Thompson [emph{Israel J. Math.} textbf{192} (2012), no. 2, 785--817]. Elaborating on our examples we prove that sufficient conditions for every shift factor of a shift space to be intrinsically ergodic given by Climenhaga and Thompson are in some sense best possible, moreover, the weak specification property neither implies intrinsic ergodicity, nor follows from almost specification. We also construct a dynamical system with the weak specification property, which does not have the almost specification property. We prove that the minimal points are dense in the support of any invariant measure of a system with the almost specification property. Furthermore, if a system with almost specification has an invariant measure with non-trivial support, then it also has uniform positive entropy over the support of any invariant measure and can not be minimal.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

<a href="/cs/project/ED1.1.00%2F02.0070" target="_blank" >ED1.1.00/02.0070: Centrum excelence IT4Innovations</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2016

Kód důvěrnosti údajů

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

Název periodika

ISR J MATH

ISSN

0021-2172

e-ISSN

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Svazek periodika

213

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

IL - Stát Izrael

Počet stran výsledku

29

Strana od-do

475-503

Kód UT WoS článku

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EID výsledku v databázi Scopus

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