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Omega-limit sets and invariant chaos in dimension one

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F16%3AN0000177" target="_blank" >RIV/47813059:19610/16:N0000177 - isvavai.cz</a>

  • Result on the web

    <a href="http://www.tandfonline.com/doi/full/10.1080/10236198.2015.1106485" target="_blank" >http://www.tandfonline.com/doi/full/10.1080/10236198.2015.1106485</a>

  • DOI - Digital Object Identifier

    <a href="http://dx.doi.org/10.1080/10236198.2015.1106485" target="_blank" >10.1080/10236198.2015.1106485</a>

Alternative languages

  • Result language

    angličtina

  • Original language name

    Omega-limit sets and invariant chaos in dimension one

  • Original language description

    Omega-limit sets play an important role in one-dimensional dynamics. During last fifty year at least three definitions of basic set has appeared. Authors often use results with different definition. Here we fill in the gap of missing proof of equivalency of these definitions. Using results on basic sets we generalize results in paper [P. Oprocha, Invariant scrambled sets and distributional chaos, Dyn. Syst. 24 (2009), no. 1, 31-43.] to the case continuous maps of finite graphs. The Li-Yorke chaos is weaker than positive topological entropy. The equivalency arises when we add condition of invariance to Li-Yorke scrambled set. In this note we show that for a continuous graph map properties positive topological entropy; horseshoe; invariant Li-Yorke scrambled set; uniform invariant distributional chaotic scrambled set and distributionaly chaotic pair are mutually equivalent.

  • Czech name

  • Czech description

Classification

  • Type

    J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

  • CEP classification

    BA - General mathematics

  • OECD FORD branch

Result continuities

  • Project

    <a href="/en/project/EE2.3.20.0002" target="_blank" >EE2.3.20.0002: Development of Research Capacities of the Mathematical Institute in Opava</a><br>

  • Continuities

    P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Others

  • Publication year

    2016

  • Confidentiality

    S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Data specific for result type

  • Name of the periodical

    Journal of Difference Equations and Applications

  • ISSN

    1023-6198

  • e-ISSN

  • Volume of the periodical

    22

  • Issue of the periodical within the volume

    3

  • Country of publishing house

    GB - UNITED KINGDOM

  • Number of pages

    6

  • Pages from-to

    468-473

  • UT code for WoS article

    000375012300007

  • EID of the result in the Scopus database

    2-s2.0-84946606994