Li-Yorke chaos for invertible mappings on compact metric spaces
Lvlin Luo, Bingzhe Hou
TL;DR
This paper demonstrates that Li-Yorke chaos in an invertible mapping on a compact metric space does not necessarily imply chaos in its inverse, using a constructed homeomorphism on the unit disk.
Contribution
It provides a counterexample showing that Li-Yorke chaos is not preserved under inversion in compact metric spaces.
Findings
Invertible Li-Yorke chaotic mappings may have non-chaotic inverses.
Constructed a specific homeomorphism on the unit disk.
Challenged assumptions about chaos preservation under inversion.
Abstract
In this paper, we construct a homeomorphism on the unit closed disk to show that an invertible mapping on a compact metric space is Li-Yorke chaotic does not imply its inverse being Li-Yorke chaotic.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Quantum chaos and dynamical systems · Advanced Differential Equations and Dynamical Systems