2020/12/27 by Fernando Argentieri, Argentieri, Fernando
Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Number Theory (math.NT) #Quantum chaos and dynamical systems #math.DS #math.NT
paper · pdf · doi:10.48550/arxiv.2012.13998
arxiv created 2020/12/27 · openalex publication_date 2020/12/27 · arxiv updated 2020/12/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let γ∈(0;(1)/(2)),τ≥ 1 and define the "γ,τ Diophantine set" as: Dγ,τ:=\α∈ (0;1): ||qα||≥\fracγqτ ∀ q∈ℕ\, ||x||:=infp∈ℤ|x-p|. In this paper we study the topology of these sets and we show that, for large τ and for almost all γ>0, Dγ,τ is a Cantor set.