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

François Maucourant (1) , Barbara Schapira (2)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée

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

Mots clés: horocycle flow; fuchsian group

Domaines: Systèmes dynamiques [math.DS]; Théorie des groupes [math.GR]

François Maucourant, Barbara Schapira. Distribution of orbits in $\R^2$ of a finitely generated group of $\SL(2,\R)$. American Journal of Mathematics, 2014, 136 (6), pp.1497-1542. ⟨hal-00690104v2⟩