Remarks on definitions of periodic points for nonautonomous dynamical system

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F19%3AA0000058" target="_blank" >RIV/47813059:19610/19:A0000058 - isvavai.cz</a>
Result on the web
<a href="https://www.tandfonline.com/doi/abs/10.1080/10236198.2019.1641496?journalCode=gdea20" target="_blank" >https://www.tandfonline.com/doi/abs/10.1080/10236198.2019.1641496?journalCode=gdea20</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1080/10236198.2019.1641496" target="_blank" >10.1080/10236198.2019.1641496</a>

Result language
angličtina
Original language name
Remarks on definitions of periodic points for nonautonomous dynamical system
Original language description
Let (X, f(1,infinity)) be a nonautonomous dynamical system. In this paper, we summarize known definitions of periodic points for general nonautonomous dynamical systems and propose a new definition of asymptotic periodicity. This definition is not only very natural but also resistant to changes of the beginning of the sequence generating the nonautonomous system. We show the relations among these definitions and discuss their properties. We prove that for pointwise convergent nonautonomous systems topological transitivity together with a dense set of asymptotically periodic points imply sensitivity. We also show that even for uniformly convergent systems, the nonautonomous analogue of Sharkovsky's theorem is not valid for most definitions of periodic points.
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
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OECD FORD branch
10101 - Pure mathematics

Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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