Local Distributional Chaos
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Local Distributional Chaos
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Qualitative Theory of Dynamical Systems
ISSN
1575-5460
e-ISSN
1662-3592
Volume of the periodical
21
Issue of the periodical within the volume
4
Country of publishing house
CH - SWITZERLAND
Number of pages
10
Pages from-to
„130-1“-„130-10“
UT code for WoS article
000855766500001
EID of the result in the Scopus database
2-s2.0-85138517363