Enroulements des géodésiques sous la mesure de Patterson-Sullivan

Nathanaël Enriquez; Jacques Franchi; Yves Le Jan

doi:10.1016/s0764-4442(98)80038-4

Enroulements des géodésiques sous la mesure de Patterson-Sullivan

Translated title of the contribution: Stable windings for geodesies under Patterson-Sullivan measure

Nathanaël Enriquez, Jacques Franchi, Yves Le Jan

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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
Original language	French
Pages (from-to)	723-726
Number of pages	4
Journal	Comptes Rendus de l'Academie des Sciences - Series I: Mathematics
Volume	326
Issue number	6
DOIs	https://doi.org/10.1016/s0764-4442(98)80038-4
State	Published - Mar 1998

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Mathematics(all)

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10.1016/s0764-4442(98)80038-4

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title = "Enroulements des g{\'e}od{\'e}siques sous la mesure de Patterson-Sullivan",

abstract = "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 M{\"o}bius isometrics associated with M.",

author = "Nathana{\"e}l Enriquez and Jacques Franchi and {Le Jan}, Yves",

year = "1998",

month = mar,

doi = "10.1016/s0764-4442(98)80038-4",

language = "French",

volume = "326",

pages = "723--726",

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T1 - Enroulements des géodésiques sous la mesure de Patterson-Sullivan

AU - Enriquez, Nathanaël

AU - Franchi, Jacques

AU - Le Jan, Yves

PY - 1998/3

Y1 - 1998/3

N2 - 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.

AB - 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.

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JF - Comptes Rendus de l'Academie des Sciences - Series I: Mathematics

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ER -

Enroulements des géodésiques sous la mesure de Patterson-Sullivan

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