Inheriting of chaos in uniformly convergent nonautonomous dynamical systems on the interval

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F16%3A%230000512" target="_blank" >RIV/47813059:19610/16:#0000512 - isvavai.cz</a>

Výsledek na webu

<a href="http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=12130" target="_blank" >http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=12130</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.3934/dcds.2016.36.3435" target="_blank" >10.3934/dcds.2016.36.3435</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Inheriting of chaos in uniformly convergent nonautonomous dynamical systems on the interval

Popis výsledku v původním jazyce

We consider nonautonomous discrete dynamical systems {f(n)}(n >= 1), where every f(n) is a surjective continuous map [0, 1] -> [0, 1] such that f(n) converges uniformly to a map f. It is well-known that f has positive topological entropy iff {f(n)}(n >=1), has. On the other hand, for systems with zero topological entropy, {f(n)}(n >= 1), with very complex dynamics can converge even to the identity map. We study the following question: Which properties of the limit function f are inherited by nonautonomous system {f(n)}(n >= 1)? We show that Li-Yorke chaos, distributional chaos DC1 and, for zero entropy maps, infinite omega-limit sets are inherited by nonautonomous systems and, for zero entropy maps, we give a criterion on f under which {f(n)}(n >= 1)is DC1. More precisely, our main results are: (i) If f is Li-Yorke chaotic then {f(n)}(n >= 1) is Li-Yorke chaotic as well, and the analogous implication is true for distributional chaos DC1; (ii) If f has zero topological entropy then th

Název v anglickém jazyce

Inheriting of chaos in uniformly convergent nonautonomous dynamical systems on the interval

Popis výsledku anglicky

We consider nonautonomous discrete dynamical systems {f(n)}(n >= 1), where every f(n) is a surjective continuous map [0, 1] -> [0, 1] such that f(n) converges uniformly to a map f. It is well-known that f has positive topological entropy iff {f(n)}(n >=1), has. On the other hand, for systems with zero topological entropy, {f(n)}(n >= 1), with very complex dynamics can converge even to the identity map. We study the following question: Which properties of the limit function f are inherited by nonautonomous system {f(n)}(n >= 1)? We show that Li-Yorke chaos, distributional chaos DC1 and, for zero entropy maps, infinite omega-limit sets are inherited by nonautonomous systems and, for zero entropy maps, we give a criterion on f under which {f(n)}(n >= 1)is DC1. More precisely, our main results are: (i) If f is Li-Yorke chaotic then {f(n)}(n >= 1) is Li-Yorke chaotic as well, and the analogous implication is true for distributional chaos DC1; (ii) If f has zero topological entropy then th

Druh

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

CEP obor

BA - Obecná matematika

OECD FORD obor

—

Projekt

<a href="/cs/project/GAP201%2F10%2F0887" target="_blank" >GAP201/10/0887: Diskrétní dynamické systémy</a><br>

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

Discrete and Continuous Dynamical Systems - Series A

ISSN

1078-0947

e-ISSN

—

Svazek periodika

36

Číslo periodika v rámci svazku

6

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

9

Strana od-do

3435-3443

Kód UT WoS článku

000371998300020

EID výsledku v databázi Scopus

2-s2.0-84954286229