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A weakly mixing dynamical system with the whole space being a transitive extremal distributionally scrambled set

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  • Wang, Lidong
  • Ou, Xiaoping
  • Gao, Yuelin

Abstract

It is known that the whole space can be a Li–Yorke scrambled set in a compact dynamical system, but this does not hold for distributional chaos. In this paper we construct a noncompact weekly mixing dynamical system, and prove that the whole space is a transitive extremal distributionally scrambled set in this system.

Suggested Citation

  • Wang, Lidong & Ou, Xiaoping & Gao, Yuelin, 2015. "A weakly mixing dynamical system with the whole space being a transitive extremal distributionally scrambled set," Chaos, Solitons & Fractals, Elsevier, vol. 70(C), pages 130-133.
    • Handle: RePEc:eee:chsofr:v:70:y:2015:i:c:p:130-133
    DOI: 10.1016/j.chaos.2014.11.012
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