On omega-limit sets of non-autonomous dynamical systems with a uniform limit of type $2^{infty}$,

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F16%3AN0000153" target="_blank" >RIV/47813059:19610/16:N0000153 - isvavai.cz</a>
Result on the web
<a href="http://www.tandfonline.com/doi/full/10.1080/10236198.2015.1123706" target="_blank" >http://www.tandfonline.com/doi/full/10.1080/10236198.2015.1123706</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1080/10236198.2015.1123706" target="_blank" >10.1080/10236198.2015.1123706</a>

Result language
angličtina
Original language name
On omega-limit sets of non-autonomous dynamical systems with a uniform limit of type $2^{infty}$,
Original language description
This paper is devoted to the study of properties of omega-limit sets of non-autonomous dynamical systems on compact metric spaces given by sequences of maps which uniformly converge to a continuous map f. We show that, for systems defined on compact metric spaces, if an omega-limit set (omega) over tilde of the non-autonomous system is a subset of the set P(f) of periodic points of f then (omega) over tilde is necessarily the union of finitely many disjoint connected sets which are cyclically mapped to one another. Using this result, we answer a question posed by Canovas in [3] [On omega-limit sets of non-autonomous systems. J. Difference Equ. Appl. 12 (2006), pp. 95-100] by proving that, if an interval map f has only finite omega-limit sets, then any omega-limit set (omega) over tilde of the non-autonomous system is a subset of the set of periodic points of f. We also show that a similar result applies to systems on trees but not on graphs with loops.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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