Distribution of orbits of geometrically finite groups acting on null vectors

Nattalie Tamam; Jacqueline M. Warren

Distribution of orbits of geometrically finite groups acting on null vectors

Dynamical Systems 2021-12-15 v5

Authors: Nattalie Tamam , Jacqueline M. Warren

Abstract

We study the distribution of non-discrete orbits of geometrically finite groups in $\operatorname{SO}(n,1)$ acting on $\mathbb{R}^{n+1}$ , and more generally on the quotient of $\operatorname{SO}(n,1)$ 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.

Keywords

geometrically finite groups orbit distribution horospherical flows SO(n,1) equidistribution

Cite

@article{arxiv.2009.11968,
  title  = {Distribution of orbits of geometrically finite groups acting on null vectors},
  author = {Nattalie Tamam and Jacqueline M. Warren},
  journal= {arXiv preprint arXiv:2009.11968},
  year   = {2021}
}

Comments

Improved readability of the paper and corrected small errors/typos. To appear in Geometriae Dedicata. 41 pages

Distribution of orbits of geometrically finite groups acting on null vectors

Abstract

Keywords

Cite

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