Counterexamples to the open problem by Zhou and Feng on the minimal centre of attraction

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F12%3A%230000359" target="_blank" >RIV/47813059:19610/12:#0000359 - isvavai.cz</a>

Výsledek na webu

<a href="http://iopscience.iop.org/0951-7715/25/5/1443/" target="_blank" >http://iopscience.iop.org/0951-7715/25/5/1443/</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1088/0951-7715/25/5/1443" target="_blank" >10.1088/0951-7715/25/5/1443</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Counterexamples to the open problem by Zhou and Feng on the minimal centre of attraction

Popis výsledku v původním jazyce

Let (X, f) be a topological dynamical system, where X is a compact metric space and f : X -> X is a continuous map. Denote by M-x the set of all invariant probability measures of f which are limit points of the sequence 1/n Sigma(n-1)(i=0) delta(fi(x)),where delta(x) is the atomic probability measure on X with support {x}. We give a characterization of points x such that M-x contains a measure whose support is C-x, the minimal centre of attraction of x, and provide examples showing that the characterization is nontrivial. In particular, the standard shift on two symbols, (Sigma(2), sigma), contains a quasi-weakly almost periodic points y, z which are not weakly almost periodic such that C-y is the support of an invariant measure and C-z is not the support of an invariant measure. This solves in negative the Open Problem 4 raised by Zhou and Feng (2004 Nonlinearity 17 493-502).

Název v anglickém jazyce

Counterexamples to the open problem by Zhou and Feng on the minimal centre of attraction

Popis výsledku anglicky

Let (X, f) be a topological dynamical system, where X is a compact metric space and f : X -> X is a continuous map. Denote by M-x the set of all invariant probability measures of f which are limit points of the sequence 1/n Sigma(n-1)(i=0) delta(fi(x)),where delta(x) is the atomic probability measure on X with support {x}. We give a characterization of points x such that M-x contains a measure whose support is C-x, the minimal centre of attraction of x, and provide examples showing that the characterization is nontrivial. In particular, the standard shift on two symbols, (Sigma(2), sigma), contains a quasi-weakly almost periodic points y, z which are not weakly almost periodic such that C-y is the support of an invariant measure and C-z is not the support of an invariant measure. This solves in negative the Open Problem 4 raised by Zhou and Feng (2004 Nonlinearity 17 493-502).

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/GAP201%2F10%2F0887" target="_blank" >GAP201/10/0887: Diskrétní dynamické systémy</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2012

Kód důvěrnosti údajů

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

Název periodika

Nonlinearity

ISSN

0951-7715

e-ISSN

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Svazek periodika

25

Číslo periodika v rámci svazku

5

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

7

Strana od-do

1443-1449

Kód UT WoS článku

000303667000012

EID výsledku v databázi Scopus

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