J
2019
Remarks on definitions of periodic points for nonautonomous dynamical system
PRAVEC, Vojtěch
Basic information
Original name
Remarks on definitions of periodic points for nonautonomous dynamical system
Authors
PRAVEC, Vojtěch (203 Czech Republic, guarantor, belonging to the institution)
Edition
Journal of Difference Equations and Applications, Abingdon, England, Taylor and Francis Ltd. 2019, 1023-6198
Other information
Type of outcome
Článek v odborném periodiku
Field of Study
10101 Pure mathematics
Country of publisher
United Kingdom of Great Britain and Northern Ireland
Confidentiality degree
není předmětem státního či obchodního tajemství
RIV identification code
RIV/47813059:19610/19:A0000058
Organization unit
Mathematical Institute in Opava
Keywords in English
Nonautonomous system; periodic point; Devaney chaos; Sharkovsky's ordering
Tags
International impact, Reviewed
V originále
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.
Displayed: 24/12/2024 15:19