On the irregular points for systems with the shadowing property

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17610%2F18%3AA1901X6Y" target="_blank" >RIV/61988987:17610/18:A1901X6Y - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1017/etds.2016.126" target="_blank" >http://dx.doi.org/10.1017/etds.2016.126</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1017/etds.2016.126" target="_blank" >10.1017/etds.2016.126</a>

Result language
angličtina
Original language name
On the irregular points for systems with the shadowing property
Original language description
We prove that when is a continuous self-map acting on a compact metric space that satisfies the shadowing property, then the set of irregular points (i.e., points with divergent Birkhoff averages) has full entropy. Using this fact, we prove that, in the class of -generic maps on manifolds, we can only observe (in the sense of Lebesgue measure) points with convergent Birkhoff averages. In particular, the time average of atomic measures along orbits of such points converges to some Sinai-Ruelle-Bowen-like measure in the weak topology. Moreover, such points carry zero entropy. In contrast, irregular points are non-observable but carry infinite entropy.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/LQ1602" target="_blank" >LQ1602: IT4Innovations excellence in science</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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