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

Carlos Matheus

doi:10.5802/crmath.65

Systèmes dynamiques

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

Carlos Matheus ¹

¹ CMLS, CNRS, École polytechnique, Institut Polytechnique de Paris, 91128 Palaiseau Cedex, France

Comptes Rendus. Mathématique, Volume 358 (2020) no. 4, pp. 475-479.

Résumé

The initial portion of the Lagrange spectrum $L_{B 7}$ 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 $L_{B 7}$ is an isolated point $ϕ_{1}$ , but the second smallest value $ϕ_{2}$ of $L_{B 7}$ is an accumulation point. Also, they conjectured that the portion $L_{B 7} \cap [ϕ_{2}, η_{1})$ is a Cantor set for a specific value $η_{1}$ and they asked about the continuity properties of the Hausdorff dimension of $L_{B 7} \cap (- \infty, t)$ as a function of $t < η_{1}$ . In this note, we solve affirmatively these problems.

Reçu le : 2020-04-22
Révisé le : 2020-04-27
Accepté le : 2020-04-27
Publié le : 2020-07-28

DOI : 10.5802/crmath.65

Affiliations des auteurs :

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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     title = {The beginning of the {Lagrange} spectrum of certain origamis of genus two},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {475--479},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {358},
     number = {4},
     year = {2020},
     doi = {10.5802/crmath.65},
     language = {en},
}

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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/

Bibliographie
Cité par

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