Remarks on uniform recurrence properties for beta-transformation

2025/12/02 by Yann Bugeaud, Bugeaud, Yann
Computer Science · Mathematics · #11J82 #37A45 #37B20 #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT) #advanced mathematical theories #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2512.02620

openalex publication_date 2025/12/02 · openalex created_date 2025/12/04 · openalex updated_date 2026/07/28

Abstract

We complement the recent paper of Zheng and Wu [Uniform recurrence properties for beta-transformation, Nonlinearity 33 (2020), 4590--4612], where the authors study, from the metrical point of view, the uniform recurrence properties of the orbit of a point under the β-transformation to the point itself.

Citations

• Combinatorial structure of Sturmian words and continued fraction expansions of Sturmian numbers
• Exponents of Diophantine approximation

Related

• Dynamical properties of the negative beta transformation
• Linear recursive odometers and beta-expansions
• Quantitative recurrence for T,T^-1 tranformation
• Quantitative recurrence properties for systems with non-uniform structure
• Uniform Diophantine approximation related to beta-transformations