Topological multiple recurrence of weakly mixing minimal systems for generalized polynomials

2021/01/18 by Ruifeng Zhang, Jianjie Zhao, Zhang, Ruifeng +1
Mathematics · #Advanced Topology and Set Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Limits and Structures in Graph Theory #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2101.06959

openalex publication_date 2021/01/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let (X, T) be a weakly mixing minimal system, p₁, ⋯, p_d be integer-valued generalized polynomials and (p₁,p₂,⋯,p_d) be non-degenerate. Then there exists a residual subset X₀ of X such that for all x∈ X₀ \ (T^p₁(n)x, ⋯, T^p_d(n)x): n∈ ℤ\ is dense in X^d.

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