no. 1
Variations on a theorem of Birman and Series
[Variations sur un théorème de Birman et Series]
Lenzhen, Anna1 ; Souto, Juan1
1 IRMAR, Université de Rennes 1 Beaulieu - Bâtiment 22-23 263, avenue du Général Leclerc 35042 Rennes CEDEX (France)
Annales de l'Institut Fourier, Tome 68 (2018) no. 1, pp. 171-194.

Soient Σ une surface hyperbolique et f:ℝ + →ℝ + une fonction monotone. Nous étudions l’adherence dans le fibré projectif tangent PTΣ de l’ensemble des géodésiques γ telles que i(γ,γ)≤f(ℓ Σ (γ)). En particulier nous montrons que si f est non bornée et sous-linéaire alors la dimension de Hausdorff de cet ensemble est strictement entre 1 et 3.

Suppose that Σ is a hyperbolic surface and f:ℝ + →ℝ + a monotonic function. We study the closure in the projective tangent bundle PTΣ of the set of all geodesics γ satisfying I(γ,γ)≤f(ℓ Σ (γ)). For instance we prove that if f is unbounded and sublinear then this set has Hausdorff dimension strictly bounded between 1 and 3.

Reçu le :
Révisé le :
Accepté le :
Publié le :
DOI : 10.5802/aif.3156
Classification : 30F10, 30F60
Keywords: geodesics, hyperbolic surface, self-intersection, Hausdorff dimension
Mot clés : géodesiques, surfaces hyperboliques, auto-intersection, dimension de Hausdorff

Lenzhen, Anna 1 ; Souto, Juan 1

1 IRMAR, Université de Rennes 1 Beaulieu - Bâtiment 22-23 263, avenue du Général Leclerc 35042 Rennes CEDEX (France)
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     title = {Variations on a theorem of {Birman} and {Series}},
     journal = {Annales de l'Institut Fourier},
     pages = {171--194},
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Lenzhen, Anna; Souto, Juan. Variations on a theorem of Birman and Series. Annales de l'Institut Fourier, Tome 68 (2018) no. 1, pp. 171-194. doi : 10.5802/aif.3156. https://aif.centre-mersenne.org/articles/10.5802/aif.3156/

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