2022
Local Distributional Chaos
BALIBREA, Francisco a Lenka RUCKÁZákladní údaje
Originální název
Local Distributional Chaos
Autoři
BALIBREA, Francisco (724 Španělsko) a Lenka RUCKÁ (203 Česká republika, garant, domácí)
Vydání
Qualitative Theory of Dynamical Systems, Basel, Switzerland, Springer Basel AG, 2022, 1575-5460
Další údaje
Jazyk
angličtina
Typ výsledku
Článek v odborném periodiku
Obor
10101 Pure mathematics
Stát vydavatele
Švýcarsko
Utajení
není předmětem státního či obchodního tajemství
Kód RIV
RIV/47813059:19610/22:A0000114
Organizační jednotka
Matematický ústav v Opavě
UT WoS
000855766500001
Klíčová slova anglicky
Distributional chaos; Symbolic space; Chaos for interval maps; Chaos for triangular maps
Štítky
Příznaky
Mezinárodní význam, Recenzováno
Změněno: 4. 3. 2023 12:19, Mgr. Aleš Ryšavý
Anotace
V originále
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.