Variations on a theorem of Birman and Series
Annales de l'Institut Fourier, Volume 68 (2018) no. 1, p. 171-194
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.
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.
Received : 2015-12-18
Revised : 2017-02-01
Accepted : 2017-03-15
Published online : 2018-04-18
DOI : https://doi.org/10.5802/aif.3156
Classification:  30F10,  30F60
Keywords: geodesics, hyperbolic surface, self-intersection, Hausdorff dimension
@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},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {68},
     number = {1},
     year = {2018},
     pages = {171-194},
     doi = {10.5802/aif.3156},
     language = {en},
     url = {https://aif.centre-mersenne.org/item/AIF_2018__68_1_171_0}
}
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/item/AIF_2018__68_1_171_0/

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