Chaos for Discrete Dynamical System

Chaos for Discrete Dynamical System

We prove that a dynamical system is chaotic in the sense of Martelli and Wiggins, when it is a transitive distributively chaotic in a sequence. Then, we give a sufficient condition for the dynamical system to be chaotic in the strong sense of Li-Yorke. We also prove that a dynamical system is distri...

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Veröffentlicht in:Journal of Applied Mathematics 2013-01, Vol.2013 (2013), p.1021-1024-097
Hauptverfasser: Wang, Lidong, Gao, Yuelin, Liu, Heng
Format: Artikel
Sprache:eng
Schlagworte:
Chaos theory
Dynamical systems
Mathematical analysis
Sequences
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Zusammenfassung:We prove that a dynamical system is chaotic in the sense of Martelli and Wiggins, when it is a transitive distributively chaotic in a sequence. Then, we give a sufficient condition for the dynamical system to be chaotic in the strong sense of Li-Yorke. We also prove that a dynamical system is distributively chaotic in a sequence, when it is chaotic in the strong sense of Li-Yorke.
ISSN:1110-757X
1687-0042
DOI:10.1155/2013/212036