The gap distribution of directions in some Schottky groups

TL;DR

This paper investigates the distribution of directions of orbits in certain Schottky groups acting on hyperbolic space, establishing the existence and properties of their limiting gap distribution functions.

Contribution

It introduces new results on the limiting gap distribution functions for directions in specific infinite covolume subgroups of isometries of hyperbolic space.

Findings

Proves the existence of limiting gap distribution functions.

Characterizes properties of these distribution functions.

Provides insights into the geometric structure of Schottky groups.

Abstract

We prove the existence and some properties of the limiting gap distribution functions for the directions of orbits of some infinite covolume subgroups of $Isom(\mathbb{H}^2)$ in the Poincar\'e disk.