On dynamics of graph maps with zero topological entropy

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
On dynamics of graph maps with zero topological entropy
Original language description
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.
Czech name
—
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
10101 - Pure mathematics

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

Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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