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Annales de l'ENS, 2014, Volume 47, Issue 5, Pages 851–903 (Mi aens1)  

Limit Theorems for Horocycle Flows

Alexander Bufetov, Giovanni Forni


Abstract: 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 representation theory methods developed in [12] for the classification of invariant distributions, the solution of the cohomological equation and the asymptotics of ergodic averages of horocycle flows.

Full text: http://smf4.emath.fr/.../ens_ann-sc_47_851-903.php
MSC: 37A17, 60F99
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