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arXiv · 1104.4502

Limit Theorems for Horocycle Flows

Alexander Bufetov·Giovanni Forni
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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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Alexander Bufetov, Giovanni Forni. 2011-04-22. Limit Theorems for Horocycle Flows. https://arxiv.org/abs/1104.4502

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