Billiard algebra, integrable line congruences, and double reflection nets
Exactly Solvable and Integrable Systems
2013-01-01 v2 Algebraic Geometry
Dynamical Systems
Abstract
The billiard systems within quadrics, playing the role of discrete analogues of geodesics on ellipsoids, are incorporated into the theory of integrable quad-graphs. An initial observation is that the Six-pointed star theorem, as the operational consistency for the billiard algebra, is equivalent to an integrabilty condition of a line congruence. A new notion of the double-reflection nets as a subclass of dual Darboux nets associated with pencils of quadrics is introduced, basic properies and several examples are presented. Corresponding Yang-Baxter maps, associated with pencils of quadrics are defined and discussed.
Cite
@article{arxiv.1112.5860,
title = {Billiard algebra, integrable line congruences, and double reflection nets},
author = {Vladimir Dragovic and Milena Radnovic},
journal= {arXiv preprint arXiv:1112.5860},
year = {2013}
}
Comments
18 pages, 8 figures