The Existence of a Billiard Orbit in the Regular Hyperbolic Simplex

TL;DR

This paper proves the existence of a specific periodic billiard path inside a regular hyperbolic simplex that touches each facet exactly once, expanding understanding of billiard dynamics in hyperbolic geometry.

Contribution

It establishes the existence of a special (n+1)-periodic billiard trajectory in hyperbolic simplices, a novel result in hyperbolic billiard dynamics.

Findings

Existence of a (n+1)-periodic billiard trajectory in hyperbolic simplices

Trajectory hits each facet exactly once

Advances understanding of billiard paths in hyperbolic geometry

Abstract

In this note we establish the existence of a (n+1)-periodic billiard trajectory inside an n-dimensional regular simplex in the hyperbolic space, which hits the interior of every facet exactly once.