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 Hölder
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.
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Meeting-ID: 652 6661 0508
Kenncode: 225657
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Asymptotics and limit theorems for horocycle flows
28.01.2022 17:00 - 18:00
Organiser:
H. Bruin, R. Zweimüller
Location:
zoom-meeting