English

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 22-dimensional case, the lattice is regular and it incorporates dynamics both in the original space and its dual. In the 33-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