Davide Ravotti (University of Vienna):
Title:
Asymptotics and limit theorems for horocycle flows
Abstract:
We present a new method to study ergodic integrals for horocycle flows which does not rely on the study of the cohomological equation. The approach is inspired by Ratner's work on quantitative mixing for the geodesic flow. We derive an explicit asymptotic expansion for horocycle averages, recovering a celebrated result by Flaminio and Forni, and we strengthen it by showing that the coefficients in the expansion are HÃ¶lder continuous with respect to the base point.
We will then explain the distributional limit theorems that can be deduced from this result, in particular we will present streamlined proofs of Bufetov and Forni's spatial limit theorem and Dolgopyat and Sarig's temporal limit theorem.