Isolated points of Diophantine sets

2020/11/20 by Fernando Argentieri, Argentieri, Fernando · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Chaos-based Image/Signal Encryption #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #math.DS #math.NT

paper · pdf · doi:10.48550/arxiv.2011.10267

arxiv created 2020/11/20 · arxiv updated 2020/11/24

Abstract

Let γ∈(0;(1)/(2)),τ≥ 1 and define the "γ,τ Diophantine set" as: D_{γ, τ}:=\α∈ (0;1): ||qα||≥\fracγq^τ ∀ q∈ℕ\, ||x||:=inf_p∈ℤ|x-p|. We analyze the topology of these sets and we show that generally they have isolated points.

Cited by

• Diophantine sets in general are Cantor sets

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