Limit Theorems for horocycle flows (joint work with Giovanni Forni)

The talk is based on joint work with Giovanni Forni and devoted to limit theorems for horocycle flows on compact surfaces of constant negative curvature. One of the main objects of the talk 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 talk is based on the preprint http://arxiv.org/pdf/1104.4502.