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Chaos in nonautonomous discrete dynamical systems approached by their subsystems
SHI Yuming * #
School of Mathematics, Shandong University, JiNan 250100
*Correspondence author
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Funding: This research was partially supported by the RFDP of Higher Education of China （No.Grant 20100131110024）, the NNSF of China （No.Grant 11071143）, the NNSF of Shandong Province （No.Grant ZR2011AM002）
Opened online:25 April 2012
Accepted by: none
Citation: SHI Yuming.Chaos in nonautonomous discrete dynamical systems approached by their subsystems[OL]. [25 April 2012] http://en.paper.edu.cn/en_releasepaper/content/4475266
 
 
A nonautonomous discrete dynamical systemis generated by a given sequence of maps. A new type of subsystem of it isintroduced. It is generated by a sequence of mapsthat are partial compositions of the given sequence of maps in the original orderso that every orbit of the subsystem is a part of anorbit of the original system starting from a same initial point.A concept of chaos in the strong sense of Wiggins is introduced.Some close relationships between chaotic dynamical behaviorsof the original system and its subsystems are given, includingchaos in the (strong) sense of Li-Yorke and Wiggins.By applying these relationships, several criteria of chaos are establishedand some sufficient conditions for no chaos are given for nonautonomous discrete systems.
Keywords:Chaos; nonautonomous discrete dynamical system; subsystem; chaos in the strong sense of Wiggins
 
 
 

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