Topologically mildly mixing of higher orders along generalized polynomials

2024/01/08 by Yang Cao, Jianjie Zhao, Cao, Yang +1
Mathematics · #Mathematical Dynamics and Fractals #Advanced Topology and Set Theory #Advanced Differential Equations and Dynamical Systems

paper · pdf · doi:10.48550/arxiv.2401.03843

Abstract

This paper is devoted to studying the multiple recurrent property of topologically mildly mixing systems along generalized polynomials. We show that if a minimal system is topologically mildly mixing, then it is mild mixing of higher orders along generalized polynomials. Precisely, suppose that (X, T) is a topologically mildly mixing minimal system, d∈ ℕ, p₁, …, p_d are integer-valued generalized polynomials with (p₁, …, p_d) non-degenerate. Then for all non-empty open subsets U , V₁, …, V_d of X, \n∈ \Z: U∩ T^-p₁(n) V₁ ∩ … ∩ T^-p_d(n) V_d ≠ ∅ \ is an IP^*-set.

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