We study the distribution of non-discrete orbits of geometrically finite groups in SO (n, 1) acting on Rn+1, and more generally on the quotient of SO (n, 1) by a horospherical subgroup. Using equidistribution of horospherical flows, we obtain both asymptotics for the distribution of orbits for the action of general geometrically finite groups, and we obtain quantitative statements with additional assumptions.
- Discrete subgroups of Lie groups
- Ergodic theory
- Flows in homogeneous spaces
- Homogeneous dynamics