Compact non-uniformizable Li-Yorke chaotic dynamical systems via an example

2025/12/22 by Mehrnaz Pourattar, Pourattar, Mehrnaz, Fatemah Ayatollah Zadeh Shirazi +1
Mathematics · Physics and Astronomy · #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #Chaos control and synchronization

paper · doi:10.48550/arxiv.2512.19881

Abstract

The main aim of this paper is extending the concept of scambled pair and Li--Yorke chaos to non--uniform compact dynamical systems. We show for finite (compact Alexandroff) topological space X with at least two elements the following statements are equivalent: \bullet one--sided shift σ:X^ℕ→ X^ℕ is Li--Yorke chaotic, \bullet one--sided shift σ:X^ℕ→ X^ℕ has at least one scrambled pair, \bullet one--sided shift σ:X^ℕ→ X^ℕ has at least one non--asymptotic pair, \bullet there exists a,b∈ X such that \a\∩\b\=\varnothing, \bullet \bigcap\\a\:a∈ X\=\varnothing.

Citations

• Li-Yorke chaos for invertible mappings on compact metric spaces
• On The Number Of Topologies On A Finite Set

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