Remarks on definitions of periodic points for nonautonomous dynamical system

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F19%3AA0000058" target="_blank" >RIV/47813059:19610/19:A0000058 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.tandfonline.com/doi/abs/10.1080/10236198.2019.1641496?journalCode=gdea20" target="_blank" >https://www.tandfonline.com/doi/abs/10.1080/10236198.2019.1641496?journalCode=gdea20</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1080/10236198.2019.1641496" target="_blank" >10.1080/10236198.2019.1641496</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Remarks on definitions of periodic points for nonautonomous dynamical system

Popis výsledku v původním jazyce

Let (X, f(1,infinity)) be a nonautonomous dynamical system. In this paper, we summarize known definitions of periodic points for general nonautonomous dynamical systems and propose a new definition of asymptotic periodicity. This definition is not only very natural but also resistant to changes of the beginning of the sequence generating the nonautonomous system. We show the relations among these definitions and discuss their properties. We prove that for pointwise convergent nonautonomous systems topological transitivity together with a dense set of asymptotically periodic points imply sensitivity. We also show that even for uniformly convergent systems, the nonautonomous analogue of Sharkovsky's theorem is not valid for most definitions of periodic points.

Název v anglickém jazyce

Remarks on definitions of periodic points for nonautonomous dynamical system

Popis výsledku anglicky

Let (X, f(1,infinity)) be a nonautonomous dynamical system. In this paper, we summarize known definitions of periodic points for general nonautonomous dynamical systems and propose a new definition of asymptotic periodicity. This definition is not only very natural but also resistant to changes of the beginning of the sequence generating the nonautonomous system. We show the relations among these definitions and discuss their properties. We prove that for pointwise convergent nonautonomous systems topological transitivity together with a dense set of asymptotically periodic points imply sensitivity. We also show that even for uniformly convergent systems, the nonautonomous analogue of Sharkovsky's theorem is not valid for most definitions of periodic points.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2019

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

1563-5120

Svazek periodika

25

Číslo periodika v rámci svazku

9-10

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

10

Strana od-do

1372-1381

Kód UT WoS článku

000476334700001

EID výsledku v databázi Scopus

2-s2.0-85075704610