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Kato’s chaos in set-valued discrete systems

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  • Gu, Rongbao

Abstract

In this paper, we investigate the relationships between Kato’s chaoticity of a dynamical system (X,f) and Kato’s chaoticity of the set-valued discrete system (K(X),f¯) associated to (X,f), where X is a compact metric space and f:X→X is a continuous map. We show that Kato’s chaoticity of (K(X),f¯) implies the Kato’s chaoticity of (X,f) in general and (X,f) is chaotic in the sense of Kato if and only if (K(X),f¯) is Kato chaotic in we-topology. We also show that Ruelle–Takens’ chaoticity implies Kato’s chaoticity for a continuous map with a fixed point from a complete metric space without isolated point into itself.

Suggested Citation

  • Gu, Rongbao, 2007. "Kato’s chaos in set-valued discrete systems," Chaos, Solitons & Fractals, Elsevier, vol. 31(3), pages 765-771.
    • Handle: RePEc:eee:chsofr:v:31:y:2007:i:3:p:765-771
    DOI: 10.1016/j.chaos.2005.10.041
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