Strange distributionally chaotic triangular maps II

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F06%3A%230000052" target="_blank" >RIV/47813059:19610/06:#0000052 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Strange distributionally chaotic triangular maps II
Original language description
The notion of distributional chaos was introduced by Schweizer and Smítal [Measures of chaos and a spectral decomposition of dynamical systems on the interval, Trans Am Math Soc 1994;344:737?854] for continuous maps of the interval. For continuous maps of a compact metric space three mutually non-equivalent versions of distributional chaos, DC1?DC3, can be considered. In this paper we study distributional chaos in the class $mathcal{T}_{m}$ of triangular maps of the square which are monotone on the fibres. The main results: (i) If $Finmathcal{T}_{m}$ has positive topological entropy then F is DC1, and hence, DC2 and DC3. This result is interesting since similar statement is not true for general triangular maps of the square [Smítal and Štefánková, Distributional chaos for triangular maps, Chaos, Solitons & Fractals 2004;21:1125?8]. (ii) There are $F_1,F_2inmathcal{T}_{m}$ which are not DC3, and such that not every recurrent point of F1 is uniformly recurrent ...
Czech name
Podivná distribučně chaotická trojúhelníková zobrazení II
Czech description
Hlavní výsledek: když trojúhelníkové zobrazení čtverce monotónní na vláknech má kladnou topologickou entropii, tak je silně distribučně chaotické.

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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Project
<a href="/en/project/GA201%2F03%2F1153" target="_blank" >GA201/03/1153: Dynamical systems II.</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year
2006
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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