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Hausdorff dimension of the sets of Li-Yorke pairs for some chaotic dynamical systems including A-coupled expanding systems

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  • Kim, Jinhyon
  • Ju, Hyonhui

Abstract

In this paper we consider Hausdorff dimension of the sets of Li-Yorke pairs for some chaotic dynamical systems including A-coupled expanding systems. We prove that Li-Yorke pairs of A-coupled-expanding system under some conditions have full Hausdorff dimension in the invariant set. Moreover we give a generalization of the result of [5] which is on the Hausdorff dimension of Li-Yorke pairs of dynamical systems topologically conjugate to the full shift and have a self-similar invariant set, to the case of the dynamical systems topologically semi-conjugate to some kinds of subshifts. Furthermore Hausdorff dimension of “chaotic invariant set” for some kinds of A-coupled-expanding maps is shown.

Suggested Citation

  • Kim, Jinhyon & Ju, Hyonhui, 2018. "Hausdorff dimension of the sets of Li-Yorke pairs for some chaotic dynamical systems including A-coupled expanding systems," Chaos, Solitons & Fractals, Elsevier, vol. 109(C), pages 246-251.
    • Handle: RePEc:eee:chsofr:v:109:y:2018:i:c:p:246-251
    DOI: 10.1016/j.chaos.2018.02.021
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    References listed on IDEAS

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    1. Shi, Yuming & Yu, Pei, 2006. "Study on chaos induced by turbulent maps in noncompact sets," Chaos, Solitons & Fractals, Elsevier, vol. 28(5), pages 1165-1180.
    2. Shi, Yuming & Ju, Hyonhui & Chen, Guanrong, 2009. "Coupled-expanding maps and one-sided symbolic dynamical systems," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2138-2149.
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    Cited by:

    1. Cui, Li & Luo, Wenhui & Ou, Qingli, 2021. "Analysis of basins of attraction of new coupled hidden attractor system," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).

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