Asymptotics and limit theorems for horocycle ergodic integrals à la Ratner

Abstract

In this talk I will present a simple method, inspired by the works of Ratner and Burger, to study ergodic integrals for the classical horocycle flow. The asymptotic expansion we can prove following this approach is a strengthening of the result by Flaminio and Forni in two ways: the coefficients in the expansion are shown to be Hölder continuous with respect to the base point and the term corresponding to the functions in the kernel of the Casimir operator is explicitly described.

Furthermore, we recover the spatial limit theorems by Bufetov and Forni and the temporal limit theorem by Dolgopyat and Sarig (this latter proof is by E. Corso).

Speaker

Davide Ravotti is a Postdoctoral Researcher at the Faculty of Mathematics of the University of Vienna.

https://davideravotti.github.io/