Geodesic
Inhomogeneous Diophantine approximation and angular recurrence for
Sbornik. Mathematics, Tome 194 (2003) no. 2, pp. 295-309

Voir la notice de l'article provenant de la source Math-Net.Ru

For a fixed rotation number we compute the Hausdorff dimension of the set of well approximable numbers. We use this result and an inhomogeneous version of Jarnik's theorem to demonstrate strong recurrence properties of the billiard flow in certain polygons. 
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     author = {S. Troubetzkoy and J. Schmeling},
     title = {Inhomogeneous {Diophantine} approximation and angular recurrence for},
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S. Troubetzkoy; J. Schmeling. Inhomogeneous Diophantine approximation and angular recurrence for. Sbornik. Mathematics, Tome 194 (2003) no. 2, pp. 295-309. http://geodesic.mathdoc.fr/item/SM_2003_194_2_a6/