PRAVEC, Vojtěch. Remarks on definitions of periodic points for nonautonomous dynamical system. Journal of Difference Equations and Applications. Abingdon, England: Taylor and Francis Ltd., 2019, roč. 25, 9-10, s. 1372-1381. ISSN 1023-6198. Dostupné z: https://dx.doi.org/10.1080/10236198.2019.1641496. |
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@article{32841, author = {Pravec, Vojtěch}, article_location = {Abingdon, England}, article_number = {9-10}, doi = {http://dx.doi.org/10.1080/10236198.2019.1641496}, keywords = {Nonautonomous system; periodic point; Devaney chaos; Sharkovsky's ordering}, language = {eng}, issn = {1023-6198}, journal = {Journal of Difference Equations and Applications}, title = {Remarks on definitions of periodic points for nonautonomous dynamical system}, url = {https://www.tandfonline.com/doi/abs/10.1080/10236198.2019.1641496?journalCode=gdea20}, volume = {25}, year = {2019} }
TY - JOUR ID - 32841 AU - Pravec, Vojtěch PY - 2019 TI - Remarks on definitions of periodic points for nonautonomous dynamical system JF - Journal of Difference Equations and Applications VL - 25 IS - 9-10 SP - 1372-1381 EP - 1372-1381 PB - Taylor and Francis Ltd. SN - 10236198 KW - Nonautonomous system KW - periodic point KW - Devaney chaos KW - Sharkovsky's ordering UR - https://www.tandfonline.com/doi/abs/10.1080/10236198.2019.1641496?journalCode=gdea20 L2 - https://www.tandfonline.com/doi/abs/10.1080/10236198.2019.1641496?journalCode=gdea20 N2 - 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. ER -
PRAVEC, Vojtěch. Remarks on definitions of periodic points for nonautonomous dynamical system. \textit{Journal of Difference Equations and Applications}. Abingdon, England: Taylor and Francis Ltd., 2019, roč.~25, 9-10, s.~1372-1381. ISSN~1023-6198. Dostupné z: https://dx.doi.org/10.1080/10236198.2019.1641496.
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