2022/09/02 by Byung-Chul Cha, Cha, Byungchul, Dong Han Kim +1
Engineering · Mathematics · #11J06 #11J17 #Advanced Numerical Analysis Techniques #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2209.00848
openalex publication_date 2022/09/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We study Lagrange spectra arising from intrinsic Diophantine approximation of circles and spheres. More precisely, we consider three circles embedded in ℝ2 or ℝ3 and three spheres embedded in ℝ3 or ℝ4. We present a unified framework to connect the Lagrange spectra of these six spaces with the spectra of ℝ and ℂ. Thanks to prior work of Asmus L.~Schmidt on the spectra of ℝ and ℂ, we obtain as a corollary, for each of the six spectra, the smallest accumulation point and the initial discrete part leading up to it completely.