Constructing the Hyperbolic Plane as the reduction of a three-body problem

Abstract

We construct the hyperbolic plane with its geodesic flow as the scale plus symmetry reduction of a three-body problem in the Euclidean plane. The potential is $-I/{\Delta }^2$ where $I$ is the triangle's moment of inertia and $\Delta$ its area. The reduction method uses the Jacobi-Maupertuis metric, following the author's earlier paper "Putting Hyperbolic Pants on a Three-body Problem".

6 pages, 1 figure

Cited by in corpus (1)

• Classical $n$-body system in geometrical and volume variables. I. Three-body case