Distribution of orbits in \R² of a finitely generated group of \SL(2,\R)

2012/04/23 by François Maucourant, Maucourant, François, Barbara Schapira +1
Mathematics · #Advanced Algebra and Geometry #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Group Theory (math.GR) #Mathematical Dynamics and Fractals #math.DS #math.GR

paper · pdf · doi:10.48550/arxiv.1204.5158

arxiv created 2012/04/23 · openalex publication_date 2012/04/23 · arxiv updated 2012/04/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this work, we study the asymptotic distribution of the non discrete orbits of a finitely generated group acting linearly on \R². To do this, we establish new equidistribution results for the horocyclic flow on the unitary tangent bundle of the associated surface.

Related

• Distribution of orbits of geometrically finite groups acting on null vectors
• Equidistribution of Horocyclic Flows on Complete Hyperbolic Surfaces of Finite Area
• Effective Ratner theorem for ASL(2,R) and gaps in √(n) modulo 1
• Separation of horocycle orbits on moduli space in genus 2
• Effective equidistribution for some one parameter unipotent flows