Let M be a geometrically finite hyperbolic surface having at least one cusp, and infinite volume. We obtain the limit law under the Patterson-Sullivan measure on T1 M of the normalized integral along the geodesies of M of any 1-form closed near the cusps. This limit law is stable with parameter 2δ - 1, where δ is the Hausdorff dimension of the limit set of the subgroup Γ of Möbius isometrics associated with M.
|Translated title of the contribution||Stable windings for geodesies under Patterson-Sullivan measure|
|Number of pages||4|
|Journal||Comptes Rendus de l'Academie des Sciences - Series I: Mathematics|
|State||Published - Mar 1998|
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