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
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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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
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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