Slow polynomial mixing, dynamical Borel-Cantelli lemma and Hausdorff dimension of dynamical diophantine sets

2025/05/27 by Edouard Daviaud, Daviaud, Edouard
Mathematics · #Advanced Differential Equations and Dynamical Systems #Advanced Topology and Set Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Metric Geometry (math.MG) #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2505.21464

openalex publication_date 2025/05/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, we establish optimality results regarding the dynamical Borel-Cantelli lemma and the the Hausdorff dimension of certain dynamical diophantine sets.

Citations

• Dimension via Waiting time and Recurrence
• Dynamical Borel-Cantelli lemmas for Gibbs measures
• The Shrinking Target Problem for Matrix Transformations of Tori: revisiting the standard problem

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