Systèmes dynamiques
The beginning of the Lagrange spectrum of certain origamis of genus two
Comptes Rendus. Mathématique, Tome 358 (2020) no. 4, pp. 475-479.

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 ${\phi }_{1}$, but the second smallest value ${\phi }_{2}$ of ${L}_{B7}$ is an accumulation point. Also, they conjectured that the portion ${L}_{B7}\cap \left[{\phi }_{2},{\eta }_{1}\right)$ is a Cantor set for a specific value ${\eta }_{1}$ and they asked about the continuity properties of the Hausdorff dimension of ${L}_{B7}\cap \left(-\infty ,t\right)$ as a function of $t<{\eta }_{1}$. In this note, we solve affirmatively these problems.

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DOI : https://doi.org/10.5802/crmath.65
@article{CRMATH_2020__358_4_475_0,
author = {Carlos Matheus},
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},
}
Carlos Matheus. The beginning of the Lagrange spectrum of certain origamis of genus two. Comptes Rendus. Mathématique, Tome 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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