Local Distributional Chaos

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F22%3AA0000114" target="_blank" >RIV/47813059:19610/22:A0000114 - isvavai.cz</a>

Výsledek na webu

<a href="https://link.springer.com/article/10.1007/s12346-022-00661-3" target="_blank" >https://link.springer.com/article/10.1007/s12346-022-00661-3</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s12346-022-00661-3" target="_blank" >10.1007/s12346-022-00661-3</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Local Distributional Chaos

Popis výsledku v původním jazyce

Distributional chaos was introduced in Schweizer and Smftal (Trans Am Math Soc 344:737-754, 1994) for continuous maps of the interval, as chaotic behavior based on development of distances between the orbits of points in the system. In Balibrea et al. (Chaos Solitons Fractals 23(5):1581-1583, 2005), this phenomenon was generalized to continuous maps of compact metric space and was distinguished into three different forms, chaos DC1, DC2 and DC3. In Loranty and Pawlak (Chaos 29:013104, 2019), the local idea of such behavior is studied, which leads to the definition of distributionally chaotic points (DC-points). It is also proved in Loranty and Pawlak (2019), that for interval maps, positive topological entropy implies existence of DC1-point. In this paper this result for interval maps is strengthened; it is proved that positive topological entropy implies existence of an uncountable set of DC1-points, and moreover this set can be chosen perfect. In greater dimensions than one, we deal with triangular systems on I-2 . In this case the relationship between topological entropy and different types of distributional chaos is not clearly understood and several different results are possible. In the paper we use an example of map F given by Kolyada (Ergod Theory Dyn Syst 12:749-768, 1992) to prove that the corresponding two dimensional system (I-2 , F) has positive topological entropy but without containing DC2-points, proving that there is no concentration of DC2-chaos.

Název v anglickém jazyce

Local Distributional Chaos

Popis výsledku anglicky

Distributional chaos was introduced in Schweizer and Smftal (Trans Am Math Soc 344:737-754, 1994) for continuous maps of the interval, as chaotic behavior based on development of distances between the orbits of points in the system. In Balibrea et al. (Chaos Solitons Fractals 23(5):1581-1583, 2005), this phenomenon was generalized to continuous maps of compact metric space and was distinguished into three different forms, chaos DC1, DC2 and DC3. In Loranty and Pawlak (Chaos 29:013104, 2019), the local idea of such behavior is studied, which leads to the definition of distributionally chaotic points (DC-points). It is also proved in Loranty and Pawlak (2019), that for interval maps, positive topological entropy implies existence of DC1-point. In this paper this result for interval maps is strengthened; it is proved that positive topological entropy implies existence of an uncountable set of DC1-points, and moreover this set can be chosen perfect. In greater dimensions than one, we deal with triangular systems on I-2 . In this case the relationship between topological entropy and different types of distributional chaos is not clearly understood and several different results are possible. In the paper we use an example of map F given by Kolyada (Ergod Theory Dyn Syst 12:749-768, 1992) to prove that the corresponding two dimensional system (I-2 , F) has positive topological entropy but without containing DC2-points, proving that there is no concentration of DC2-chaos.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

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

Název periodika

Qualitative Theory of Dynamical Systems

ISSN

1575-5460

e-ISSN

1662-3592

Svazek periodika

21

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

10

Strana od-do

„130-1“-„130-10“

Kód UT WoS článku

000855766500001

EID výsledku v databázi Scopus

2-s2.0-85138517363