Irregular recurrence in compact metric spaces

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F13%3A%230000396" target="_blank" >RIV/47813059:19610/13:#0000396 - isvavai.cz</a>
Result on the web
<a href="http://www.sciencedirect.com/science/article/pii/S0960077913001240" target="_blank" >http://www.sciencedirect.com/science/article/pii/S0960077913001240</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.chaos.2013.06.010" target="_blank" >10.1016/j.chaos.2013.06.010</a>

Result language
angličtina
Original language name
Irregular recurrence in compact metric spaces
Original language description
For a continuous map f : X -> X of a compact metric space, the set IR(f) of irregularly recurrent points is the set of points which are upper density recurrent, but not lower density recurrent. These notions are related to the structure of the measure center, but many problems still remain open. We solve some of them. The main result, based on examples by Obadalova and Smital [Obadalova L, Smltal J. Counterexamples to the open problem by Zhou and Feng on minimal center of attraction. Nonlinearity 2012;25:1443-9], shows that positive topological entropy supported by the center C-z of attraction of a point z is not related to the property that C-z is the support of an invariant measure generated by z. We also show that IR(f) is invariant with respect tostandard operations, like f(IR(f)) = IR(f), or IR(f(m)) = IR(f) for m is an element of N.
Czech name
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Czech description
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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
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2013
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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