semisimple Lie groups

discrete subgroups

expanding horospherical subgroup

equidistribution results

analytic curves

application to Diophantine approximation

37-XX - Dynamical systems and ergodic theory [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX]

37Dxx - Dynamical systems with hyperbolic behavior

37D40 - Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)

11Jxx - Diophantine approximation, transcendental number theory [See also 11K60]

53A04 - Curves in Euclidean space

22A26 - Topological semilattices, lattices and applications [See also 06B30, 06B35, 06F30]

22E40 - Discrete subgroups of Lie groups [See also 20Hxx, 32Nxx]

22Exx - Lie groups {For the topology of Lie groups and homogeneous spaces, see 57Sxx, 57Txx; for analysis thereon, see 43A80, 43A85, 43A90}