Variations on a theorem of Birman and Series
[Variations sur un théorème de Birman et Series]
Annales de l'Institut Fourier, Tome 68 (2018) no. 1, pp. 171-194.

Soient Σ une surface hyperbolique et f: + + 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( 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: + + 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( 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.

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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)
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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. http://archive.numdam.org/articles/10.5802/aif.3156/

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