On M-dynamics and Li-Yorke chaos of extensions of minimal dynamics

2023/01/13 by Xiongping Dai, Dai, Xiongping · 1 citation
Mathematics · #37B05 #Advanced Differential Equations and Dynamical Systems #Classical Analysis and ODEs (math.CA) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2301.05441

openalex publication_date 2023/01/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let π\colon\mathscrX→\mathscrY be an extension of minimal compact metric flows such that R_π\not=Δ_X. A subflow of R_π is called an M-flow if it is T.T. and contains a dense set of a.p. points. In this paper we mainly prove the following: (1) π is PI iff Δ_X is the unique M-flow containing Δ_X in R_π. (2) If π is not PI, then there exists a canonical Li-Yorke chaotic M-flow in R_π. In particular, an Ellis weak-mixing non-proximal extension is non-PI and so Li-Yorke chaotic. (3) A unbounded or non-minimal M-flow, not necessarily compact, is sensitive on initial conditions. (4) every syndetically distal flow is pointwise Bohr a.p.

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