The initial portion of the Lagrange spectrum 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 is an isolated point , but the second smallest value of is an accumulation point. Also, they conjectured that the portion is a Cantor set for a specific value and they asked about the continuity properties of the Hausdorff dimension of as a function of . In this note, we solve affirmatively these problems.
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Carlos Matheus 1
@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, 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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