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Relations between distributional, Li–Yorke and ω chaos

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  • Guirao, Juan Luis García
  • Lampart, Marek

Abstract

The forcing relations between notions of distributional, Li–Yorke and ω chaos were studied by many authors. In this paper we summarize all known connections between these three different types of chaos and fulfill the results for general compact metric spaces by the construction of a selfmap on a compact perfect set which is ω chaotic, not distributionally chaotic and has zero topological entropy.

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  • Guirao, Juan Luis García & Lampart, Marek, 2006. "Relations between distributional, Li–Yorke and ω chaos," Chaos, Solitons & Fractals, Elsevier, vol. 28(3), pages 788-792.
    • Handle: RePEc:eee:chsofr:v:28:y:2006:i:3:p:788-792
    DOI: 10.1016/j.chaos.2005.08.005
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    1. García Guirao, Juan Luis & Lampart, Marek, 2005. "Li and Yorke chaos with respect to the cardinality of the scrambled sets," Chaos, Solitons & Fractals, Elsevier, vol. 24(5), pages 1203-1206.
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