On the structure of α-limit sets of backward trajectories for graph maps

Kód výsledku v IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F22%3AA0000117" target="_blank" >RIV/47813059:19610/22:A0000117 - isvavai.cz</a>
Výsledek na webu
<a href="https://www.aimsciences.org/article/doi/10.3934/dcds.2021159" target="_blank" >https://www.aimsciences.org/article/doi/10.3934/dcds.2021159</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.3934/dcds.2021159" target="_blank" >10.3934/dcds.2021159</a>

Jazyk výsledku
angličtina
Název v původním jazyce
On the structure of α-limit sets of backward trajectories for graph maps
Popis výsledku v původním jazyce
In the paper we study what sets can be obtained as alpha-limit sets of backward trajectories in graph maps. We show that in the case of mixing maps, all those alpha-limit sets are omega-limit sets and for all but finitely many points x, we can obtain every omega-limits set as the alpha-limit set of a backward trajectory starting in x. For zero entropy maps, every alpha-limit set of a backward trajectory is a minimal set. In the case of maps with positive entropy, we obtain a partial characterization which is very close to complete picture of the possible situations.
Název v anglickém jazyce
On the structure of α-limit sets of backward trajectories for graph maps
Popis výsledku anglicky
In the paper we study what sets can be obtained as alpha-limit sets of backward trajectories in graph maps. We show that in the case of mixing maps, all those alpha-limit sets are omega-limit sets and for all but finitely many points x, we can obtain every omega-limits set as the alpha-limit set of a backward trajectory starting in x. For zero entropy maps, every alpha-limit set of a backward trajectory is a minimal set. In the case of maps with positive entropy, we obtain a partial characterization which is very close to complete picture of the possible situations.

Projekt
—
Návaznosti
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění
2022
Kód důvěrnosti údajů
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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