Asymptotics and limit theorems for horocycle ergodic integrals à la Ratner

Vortrag von Davide Ravotti - Emilio Corso

Datum: 04.10.21  Zeit: 15.00 - 16.00  Raum: Y27H28

In the first part of this talk, we will 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 Hölder continuous with respect to the base point. The second part will focus on 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.