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Relations between mixing and distributional chaos

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  • Liao, Gongfu
  • Chu, Zhenyan
  • Fan, Qinjie

Abstract

Oprocha gave an example which is weakly mixing but not distributively chaotic. In this paper, we give an example which is mixing but not distributively chaotic. We also prove that if f:X→X is weakly mixing, where X is a locally compact metric space containing at least two points, then it must be distributively chaotic in a sequence.

Suggested Citation

  • Liao, Gongfu & Chu, Zhenyan & Fan, Qinjie, 2009. "Relations between mixing and distributional chaos," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1994-2000.
    • Handle: RePEc:eee:chsofr:v:41:y:2009:i:4:p:1994-2000
    DOI: 10.1016/j.chaos.2008.08.003
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    References listed on IDEAS

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    1. Balibrea, F. & Smı́tal, J. & Štefánková, M., 2005. "The three versions of distributional chaos," Chaos, Solitons & Fractals, Elsevier, vol. 23(5), pages 1581-1583.
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