Li-Yorke pairs of full Hausdorff dimension for some chaotic dynamical systems
J\"org Neunh\"auserer
TL;DR
This paper demonstrates that in certain classical chaotic dynamical systems, the set of Li-Yorke pairs occupies the entire Hausdorff dimension of invariant sets, highlighting the complexity of their chaotic behavior.
Contribution
It establishes that Li-Yorke pairs can have full Hausdorff dimension in specific chaotic systems, a novel insight into their fractal structure.
Findings
Li-Yorke pairs have full Hausdorff dimension on invariant sets
Chaotic systems exhibit highly complex Li-Yorke pair structures
Results apply to some classical chaotic dynamical systems
Abstract
We show that for some simple classical chaotic dynamical systems the set of Li-Yorke pairs has full Hausdorff dimension on invariant sets.
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