Minimal PI-systems with all points are multiply minimal

2025/11/19 by Lin, Zijie, Ouyang, Kangbo
Computer Science · Mathematics · #Cellular Automata and Applications #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #semigroups and automata theory

paper · doi:10.48550/arxiv.2511.15335

openalex publication_date 2025/11/19 · openalex created_date 2025/11/23 · openalex updated_date 2026/07/28

Abstract

We construct a minimal subshift \((X^*,σ)\) that serves as an open proximal extension of its maximal equicontinuous factor. We establish that every point in this subshift is multiply recurrent minimal. This work solves an open problem raised by Huang, Shao and Ye regarding the existence of minimal PI-systems such that each point is multiply minimal.

Citations

• Multiply minimal points for the product of iterates

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