Counterexamples to the open problem by Zhou and Feng on the minimal centre of attraction

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F12%3A%230000359" target="_blank" >RIV/47813059:19610/12:#0000359 - isvavai.cz</a>
Result on the web
<a href="http://iopscience.iop.org/0951-7715/25/5/1443/" target="_blank" >http://iopscience.iop.org/0951-7715/25/5/1443/</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1088/0951-7715/25/5/1443" target="_blank" >10.1088/0951-7715/25/5/1443</a>

Result language
angličtina
Original language name
Counterexamples to the open problem by Zhou and Feng on the minimal centre of attraction
Original language description
Let (X, f) be a topological dynamical system, where X is a compact metric space and f : X -> X is a continuous map. Denote by M-x the set of all invariant probability measures of f which are limit points of the sequence 1/n Sigma(n-1)(i=0) delta(fi(x)),where delta(x) is the atomic probability measure on X with support {x}. We give a characterization of points x such that M-x contains a measure whose support is C-x, the minimal centre of attraction of x, and provide examples showing that the characterization is nontrivial. In particular, the standard shift on two symbols, (Sigma(2), sigma), contains a quasi-weakly almost periodic points y, z which are not weakly almost periodic such that C-y is the support of an invariant measure and C-z is not the support of an invariant measure. This solves in negative the Open Problem 4 raised by Zhou and Feng (2004 Nonlinearity 17 493-502).
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
<a href="/en/project/GAP201%2F10%2F0887" target="_blank" >GAP201/10/0887: Discrete dynamical systems</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>S - Specificky vyzkum na vysokych skolach

Publication year
2012
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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