The Cohomological Equation and Invariant Distributions for Horocycle Maps

Details The Cohomological Equation and Invariant Distributions for Horocycle Maps The Cohomological Equation and Invariant Distributions for Horocycle Maps

2011-09-15

arxiv.org/abs/1109.3495v2

Mathematics

Dynamical Systems

Fixed some typos. 65 pages

Scientific paper

We study the invariant distributions for the horocycle map on
$\Gamma\backslash PSL(2, \mathbb{R})$ and prove Sobolev estimates for the
cohomological equation of the horocycle map. As an application, we obtain an
estimate for the rate of equidistribution for horocycle maps on compact
manifolds.

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