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

TL;DR

This paper investigates the Hausdorff dimension of Li-Yorke pairs in certain chaotic systems, demonstrating they often have full dimension and extending previous results to more general subshifts and A-coupled-expanding maps.

Contribution

It generalizes existing results on the Hausdorff dimension of Li-Yorke pairs to A-coupled-expanding systems and subshifts, providing new insights into their chaotic invariant sets.

Findings

Li-Yorke pairs have full Hausdorff dimension under certain conditions

Extension of previous results to systems conjugate to subshifts

Determination of Hausdorff dimension for chaotic invariant sets

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 on the invariant set. we generalize the result of [8] on the Hausdorff dimension of Li-Yorke pairs of dynamical systems topologically conjugate to the full shift and having a self-similar invariant set to the case of dynamical system conjugated to some kind of subshifts. And Hausdorff dimension of "chaotic invariant set" for some kind of A-coupled-expanding maps is shown.