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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 φ 1 , but the second smallest value φ 2 of L B7 is an accumulation point. Also, they conjectured that the portion L B7 [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 B7 (-,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 : 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},
     url = {comptes-rendus.academie-sciences.fr/mathematique/item/CRMATH_2020__358_4_475_0/}
}
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/item/CRMATH_2020__358_4_475_0/

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