References & Citations
Mathematics > Dynamical Systems
Title: Concentration of dimension in extremal points of left-half lines in the Lagrange spectrum
(Submitted on 26 Sep 2023 (v1), last revised 27 Mar 2024 (this version, v2))
Abstract: We prove that for any $\eta$ that belongs to the closure of the interior of the Markov and Lagrange spectra, the sets $k^{-1}((-\infty,\eta])$ and $k^{-1}(\eta)$, which are the sets of irrational numbers with best constant of Diophantine approximation bounded by $\eta$ and exactly $\eta$ respectively, have the same Hausdorff dimension. We also show that, as $\eta$ varies in the interior of the spectra, this Hausdorff dimension is a strictly increasing function.
Submission history
From: Christian Camilo Silva Villamil [view email][v1] Tue, 26 Sep 2023 03:55:43 GMT (21kb)
[v2] Wed, 27 Mar 2024 18:38:41 GMT (24kb)
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