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Hausdorff dimension of the sets of Li-Yorke pairs for some chaotic dynamical systems including \(A\)-coupled expanding systems. (English) Zbl 1390.37028

Summary: 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 J. Neunhäuserer [Math. Bohem. 135, No. 3, 279–289 (2010; Zbl 1224.37011)] 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.

MSC:

37B45 Continua theory in dynamics

Citations:

Zbl 1224.37011
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References:

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