Mixing sequences for non-mixing transformations and group actions

2022/06/01 by El Houcein El Abdalaoui, T. Adams, Abdalaoui, el Houcein el +1
Mathematics · #37A25 #37A30 #42A55 #43A25 #Advanced Differential Equations and Dynamical Systems #Advanced Topology and Set Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Spectral Theory (math.SP)

paper · pdf · doi:10.48550/arxiv.2206.01177

openalex publication_date 2022/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish that there are non-mixing maps that are mixing on appropriate sequences including sequences (s_i) which satisfy the Rajchman dissociated property. Our examples are based on the staircase rank one construction, M-towers constructions and the Gaussian transformations. As a consequence, we obtain there are non-mixing maps which are mixing along the squares. We further prove that a sequence M=(m_n) is a mixing sequence for some weak mixing 1/2-rigid transformation T if and only if the complement of M is a thick set. This result is generalized to r/(r+1)-rigid transformations for r∈ ℕ. Moreover, by applying Host-Parreau characterization of the set of continuity from Harmonic Analysis, we extend our results to the infinite countable abelian group actions.

Related

• Mixing sets for rigid transformations
• Mixing sets for non-mixing transformations
• Rigid-Recurrent Sequences for Actions of Finite Exponent Groups
• Mixing on Stochastic Staircase Transformations
• Strongly mixing systems are almost strongly mixing of all orders