no. 4
Systèmes dynamiques
The beginning of the Lagrange spectrum of certain origamis of genus two
Matheus, Carlos1
1 CMLS, CNRS, École polytechnique, Institut Polytechnique de Paris, 91128 Palaiseau Cedex, France
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.

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DOI : 10.5802/crmath.65
Matheus, Carlos 1

1 CMLS, CNRS, École polytechnique, Institut Polytechnique de Paris, 91128 Palaiseau Cedex, France 
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Matheus, Carlos. 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. http://www.numdam.org/articles/10.5802/crmath.65/

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