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Li and Yorke chaos with respect to the cardinality of the scrambled sets

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  • García Guirao, Juan Luis
  • Lampart, Marek

Abstract

In the present paper we study Li and Yorke chaos on several spaces in connection with the cardinality of its scrambled sets. We prove that there is a map on a Cantor set and a map on a two-dimensional arcwise connected continuum (with empty interior) such that each scrambled set contains exactly two points.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:24:y:2005:i:5:p:1203-1206
    DOI: 10.1016/j.chaos.2004.09.103
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    1. 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.

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