The beginning of the Lagrange spectrum of certain origamis of genus two

Carlos Matheus

doi:10.5802/CRMATH.65

The beginning of the Lagrange spectrum of certain origamis of genus two

Carlos Matheus

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Abstract

The initial portion of the Lagrange spectrum L_B₇ of certain square-tiled surfaces of genus two was described in details in the work of Hubert-Lelièvre-Marchese-Ulcigrai. In particular, they proved that the smallest element of L_B₇ is an isolated point φ1, but the second smallest value φ₂ of L_B₇ is an accumulation point. Also, they conjectured that the portion L_B₇ ∩[φ2,η₁) is a Cantor set for a specific value η₁ and they asked about the continuity properties of the Hausdorff dimension of L_B₇ ∩(−∞,t) as a function of t <η1. In this note, we solve affirmatively these problems.

Original language	English
Pages (from-to)	475-479
Number of pages	5
Journal	Comptes Rendus Mathematique
Volume	358
Issue number	4
DOIs	https://doi.org/10.5802/CRMATH.65
Publication status	Published - 1 Jul 2020

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The beginning of the Lagrange spectrum of certain origamis of genus two

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