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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., vol.~25, 9-10, p.~1372-1381. ISSN~1023-6198. doi:10.1080/10236198.2019.1641496. 2019.
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