Quasi-graphs, zero entropy and measures with discrete spectrum

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17610%2F22%3AA23029QB" target="_blank" >RIV/61988987:17610/22:A23029QB - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1088/1361-6544/ac4b3a" target="_blank" >http://dx.doi.org/10.1088/1361-6544/ac4b3a</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1088/1361-6544/ac4b3a" target="_blank" >10.1088/1361-6544/ac4b3a</a>

Result language
angličtina
Original language name
Quasi-graphs, zero entropy and measures with discrete spectrum
Original language description
In this paper, we study dynamics of maps on quasi-graphs and characterise their invariant measures. In particular, we prove that every invariant measure of a quasi-graph map with zero topological entropy has discrete spectrum. Additionally, we obtain an analog of Llibre-Misiurewicz's result relating positive topological entropy with existence of topological horseshoes. We also study dynamics on dendrites and show that if a continuous map on a dendrite whose set of all endpoints is closed and has only finitely many accumulation points, has zero topological entropy, then every invariant measure supported on an orbit closure has discrete spectrum
Czech name
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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
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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