Distribution of orbits in ${\mathbb{R}}^2$ of a finitely generated group of $\SL(2,\R)$

Abstract

In this work, we study the asymptotic distribution of the non discrete orbits of a finitely generated group acting linearly on ${\mathbb{R}}^2$. To do this, we establish new equidistribution results for the horocyclic flow on the unitary tangent bundle of the associated surface.