On the Weakest Version of Distributional Chaos
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F16%3AN0000152" target="_blank" >RIV/47813059:19610/16:N0000152 - isvavai.cz</a>
Result on the web
<a href="http://www.worldscientific.com/doi/abs/10.1142/S0218127416502357" target="_blank" >http://www.worldscientific.com/doi/abs/10.1142/S0218127416502357</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1142/S0218127416502357" target="_blank" >10.1142/S0218127416502357</a>
Alternative languages
Result language
angličtina
Original language name
On the Weakest Version of Distributional Chaos
Original language description
The aim of the paper is to correct and improve some results concerning distributional chaos of type 3. We show that in a general compact metric space, distributional chaos of type 3, denoted DC3, even when assuming the existence of an uncountable scrambled set, is a very weak form of chaos. In particular, (i) the chaos can be unstable (it can be destroyed by conjugacy), and (ii) such an unstable system may contain no Li-Yorke pair. However, the definition can be strengthened to get DC21/2 which is a topological invariant and implies Li-Yorke chaos, similarly as types DC1 and DC2; but unlike them, strict DC21/2 systems must have zero topological entropy.
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
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Continuities
S - Specificky vyzkum na vysokych skolach<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
International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
ISSN
0218-1274
e-ISSN
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Volume of the periodical
26
Issue of the periodical within the volume
14
Country of publishing house
SG - SINGAPORE
Number of pages
13
Pages from-to
"1650235-1"-"1650235-13"
UT code for WoS article
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EID of the result in the Scopus database
2-s2.0-85009819846