On dynamics of graph maps with zero topological entropy

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17610%2F17%3AA21020TG" target="_blank" >RIV/61988987:17610/17:A21020TG - isvavai.cz</a>

Výsledek na webu

<a href="https://iopscience.iop.org/article/10.1088/1361-6544/aa8817" target="_blank" >https://iopscience.iop.org/article/10.1088/1361-6544/aa8817</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1088/1361-6544/aa8817" target="_blank" >10.1088/1361-6544/aa8817</a>

Jazyk výsledku

angličtina

Název v původním jazyce

On dynamics of graph maps with zero topological entropy

Popis výsledku v původním jazyce

We explore the dynamics of graph maps with zero topological entropy. It is shown that a continuous map f on a topological graph G has zero topological entropy if and only if it is locally mean equicontinuous, that is the dynamics on each orbit closure is mean equicontinuous. As an application, we show that Sarnak's Mobius disjointness conjecture is true for graph maps with zero topological entropy. We also extend several results known in interval dynamics to graph maps. We show that a graph map has zero topological entropy if and only if there is no 3-scrambled tuple if and only if the proximal relation is an equivalence relation; a graph map has no scrambled pairs if and only if it is null if and only if it is tame.

Název v anglickém jazyce

On dynamics of graph maps with zero topological entropy

Popis výsledku anglicky

We explore the dynamics of graph maps with zero topological entropy. It is shown that a continuous map f on a topological graph G has zero topological entropy if and only if it is locally mean equicontinuous, that is the dynamics on each orbit closure is mean equicontinuous. As an application, we show that Sarnak's Mobius disjointness conjecture is true for graph maps with zero topological entropy. We also extend several results known in interval dynamics to graph maps. We show that a graph map has zero topological entropy if and only if there is no 3-scrambled tuple if and only if the proximal relation is an equivalence relation; a graph map has no scrambled pairs if and only if it is null if and only if it is tame.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2017

Kód důvěrnosti údajů

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

Název periodika

NONLINEARITY

ISSN

0951-7715

e-ISSN

—

Svazek periodika

30

Číslo periodika v rámci svazku

12

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

17

Strana od-do

4260-4276

Kód UT WoS článku

000414409300001

EID výsledku v databázi Scopus

2-s2.0-85036658851