Integrable lattices of hyperplanes related to billiards within confocal quadrics
Differential Geometry
2015-08-06 v1 Dynamical Systems
Metric Geometry
Exactly Solvable and Integrable Systems
Abstract
We introduce a new discrete system that arises from ellipsoidal billiards and is closely related to the double reflection nets. The system is defined on the lattice of a uniform honeycomb consisting of rectified hypercubes and cross polytopes. In the -dimensional case, the lattice is regular and it incorporates dynamics both in the original space and its dual. In the -dimensional case, the lattice consists of tetrahedra and cuboctahedra.
Keywords
Cite
@article{arxiv.1508.01027,
title = {Integrable lattices of hyperplanes related to billiards within confocal quadrics},
author = {Milena Radnovic},
journal= {arXiv preprint arXiv:1508.01027},
year = {2015}
}
Comments
6 pages, 3 figures