Suppose that is a hyperbolic surface and a monotonic function. We study the closure in the projective tangent bundle of the set of all geodesics satisfying . For instance we prove that if is unbounded and sublinear then this set has Hausdorff dimension strictly bounded between and .
Soient une surface hyperbolique et une fonction monotone. Nous étudions l’adherence dans le fibré projectif tangent de l’ensemble des géodésiques telles que . En particulier nous montrons que si est non bornée et sous-linéaire alors la dimension de Hausdorff de cet ensemble est strictement entre et .
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Accepted:
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Keywords: geodesics, hyperbolic surface, self-intersection, Hausdorff dimension
Mot clés : géodesiques, surfaces hyperboliques, auto-intersection, dimension de Hausdorff
Lenzhen, Anna 1; Souto, Juan 1
@article{AIF_2018__68_1_171_0, author = {Lenzhen, Anna and Souto, Juan}, title = {Variations on a theorem of {Birman} and {Series}}, journal = {Annales de l'Institut Fourier}, pages = {171--194}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {68}, number = {1}, year = {2018}, doi = {10.5802/aif.3156}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3156/} }
TY - JOUR AU - Lenzhen, Anna AU - Souto, Juan TI - Variations on a theorem of Birman and Series JO - Annales de l'Institut Fourier PY - 2018 SP - 171 EP - 194 VL - 68 IS - 1 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.3156/ DO - 10.5802/aif.3156 LA - en ID - AIF_2018__68_1_171_0 ER -
%0 Journal Article %A Lenzhen, Anna %A Souto, Juan %T Variations on a theorem of Birman and Series %J Annales de l'Institut Fourier %D 2018 %P 171-194 %V 68 %N 1 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.3156/ %R 10.5802/aif.3156 %G en %F AIF_2018__68_1_171_0
Lenzhen, Anna; Souto, Juan. Variations on a theorem of Birman and Series. Annales de l'Institut Fourier, Volume 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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