Volume 19, Issue 3, September 2012, Pages 300 - 317
Billiard Algebra, Integrable Line Congruences, and Double Reflection Nets
Authors
Vladimir Dragović
Mathematical Institute SANU, Kneza Mihaila 36, Belgrade, Serbia,vladad@mi.sanu.ac.rs
Milena Radnović
Mathematical Physics Group, University of Lisbon, Portugal,milena@mi.sanu.ac.rs
Received 27 December 2011, Accepted 27 March 2012, Available Online 20 September 2012.
- DOI
- 10.1142/S1402925112500192How to use a DOI?
- Keywords
- Ellipsoidal billiard; confocal quadrics; quad-graphs; integrability
- Abstract
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 integrability 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 properties and several examples are presented. Corresponding Yang–Baxter maps, associated with pencils of quadrics are defined and discussed.
- Copyright
- © 2012 The Authors. Published by Atlantis Press and Taylor & Francis
- Open Access
- This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
TY - JOUR AU - Vladimir Dragović AU - Milena Radnović PY - 2012 DA - 2012/09/20 TI - Billiard Algebra, Integrable Line Congruences, and Double Reflection Nets JO - Journal of Nonlinear Mathematical Physics SP - 300 EP - 317 VL - 19 IS - 3 SN - 1776-0852 UR - https://doi.org/10.1142/S1402925112500192 DO - 10.1142/S1402925112500192 ID - Dragović2012 ER -