2020/04/25 by Chen, Huayang, Alan Haynes, Haynes, Alan
Computer Science · Mathematics · #11J61 #11J83 #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT) #Topological and Geometric Data Analysis #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.2004.12153
openalex publication_date 2020/04/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we investigate the problem of how well points in finite dimensional p-adic solenoids can be approximated by rationals. The setting we work in was previously studied by Palmer, who proved analogues of Dirichlet's theorem and the Duffin-Schaeffer theorem. We prove a complementary result, showing that the set of badly approximable points has maximum Hausdorff dimension. Our proof is a simple application of the elegant machinery of Schmidt's game.