Comptes Rendus
no. 4
Systèmes dynamiques
The beginning of the Lagrange spectrum of certain origamis of genus two
Carlos Matheus1
1 CMLS, CNRS, École polytechnique, Institut Polytechnique de Paris, 91128 Palaiseau Cedex, France
Comptes Rendus. Mathématique, Volume 358 (2020) no. 4, pp. 475-479.

The initial portion of the Lagrange spectrum LB7 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 LB7 is an isolated point ϕ1, but the second smallest value ϕ2 of LB7 is an accumulation point. Also, they conjectured that the portion LB7∩[ϕ2,η1) is a Cantor set for a specific value η1 and they asked about the continuity properties of the Hausdorff dimension of LB7∩(-∞,t) as a function of t<η1. In this note, we solve affirmatively these problems.

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DOI : 10.5802/crmath.65

Carlos Matheus 1

1 CMLS, CNRS, École polytechnique, Institut Polytechnique de Paris, 91128 Palaiseau Cedex, France
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Carlos Matheus. The beginning of the Lagrange spectrum of certain origamis of genus two. Comptes Rendus. Mathématique, Volume 358 (2020) no. 4, pp. 475-479. doi : 10.5802/crmath.65. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.65/

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