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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

  • Czech description

Classification

  • Type

    J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database

  • CEP classification

  • OECD FORD branch

    10101 - Pure mathematics

Result continuities

  • Project

  • 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