An effective Ratner equidistribution result for SL(2,R)⋉R2

Andreas Strömbergsson

doi:10.1215/00127094-2885873

Abstract

Let $G=\operatorname{SL}(2,\mathbb{R})\ltimes\mathbb{R}^{2}$ be the affine special linear group of the plane, and set $\Gamma=\operatorname{SL}(2,\mathbb{Z})\ltimes\mathbb{Z}^{2}$ . We prove a polynomially effective asymptotic equidistribution result for the orbits of a $1$ -dimensional, nonhorospherical unipotent flow on $\Gamma \backslash G$ .

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Andreas Strömbergsson. "An effective Ratner equidistribution result for $\operatorname{SL}(2,\mathbb{R})\ltimes\mathbb{R}^{2}$ ." Duke Math. J. 164 (5) 843 - 902, 1 April 2015. https://doi.org/10.1215/00127094-2885873

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Published: 1 April 2015

First available in Project Euclid: 7 April 2015

zbMATH: 1351.37014

MathSciNet: MR3332893

Digital Object Identifier: 10.1215/00127094-2885873

Subjects:

Primary: 37A17

Secondary: 11K60 , 37A45

Keywords: effective equidistribution , horocycle , Ratner equidistribution , unipotent flow

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