Limit Theorems for Horocycle Flows

2011/04/22 by Bufetov, Alexander, Forni, Giovanni
#22E46 #37A17 #37A50 #37D40 #60B10 #Dynamical Systems (math.DS) #FOS: Mathematics #Probability (math.PR) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1104.4502

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 Hoelder 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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