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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2016

Kód důvěrnosti údajů

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

Název periodika

Journal of Difference Equations and Applications

ISSN

1023-6198

e-ISSN

—

Svazek periodika

22

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

9

Strana od-do

636-644

Kód UT WoS článku

000375012400009

EID výsledku v databázi Scopus

2-s2.0-84951263167