2025/02/06 by Hajime Kaneko, Kaneko, Hajime, Jonathan Caalim +3
Mathematics · #11J25 #11K16 #11R52 #37E05 #68R15 #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2502.04149
openalex publication_date 2025/02/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider rotational beta expansions in dimensions 1, 2 and 4 and view them as expansions on real numbers, complex numbers, and quaternions, respectively. We give sufficient conditions on the parameters α, β∈ (0,1) so that particular cylinder sets arising from the expansions are winning or losing Schmidt (α,β)-game.