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Article Dans Une Revue Annales Scientifiques de l'École Normale Supérieure Année : 2014

LIMIT THEOREMS FOR HOROCYCLE FLOWS

Résumé

The main results of this paper are limit theorems for horocycle flows on compact surfaces of constant negative curvature. One of the main objects of the paper is a special family of horocycle-invariant finitely additive Hölder measures on rectifiable arcs. An asymptotic formula for ergodic integrals for horocycle flows is obtained in terms of the finitely-additive measures, and limit theorems follow as a corollary of the asymptotic formula. The objects and results of this paper are similar to those in [15], [16], [4] and [5] for translation flows on flat surfaces. The arguments are based on the classification of invariant distributions for horocycle flows established in [12].
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hal-01256161 , version 1 (14-01-2016)

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  • HAL Id : hal-01256161 , version 1

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Alexander I. Bufetov, Giovanni Forni. LIMIT THEOREMS FOR HOROCYCLE FLOWS. Annales Scientifiques de l'École Normale Supérieure, 2014. ⟨hal-01256161⟩
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