EMIS ELibM Electronic Journals Publications de l'Institut Mathématique, Nouvelle Série
Vol. 98(112), pp. 25–30 (2015)

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Integrable lattices of hyperplanes related to billiards within confocal quadrics}

Milena Radnovic

Mathematical Institute SANU, Belgrade, Serbia; School of Mathematics and Statistics, University of Sydney, NSW, Australia

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 2-dimensional case, the lattice is regular and it incorporates dynamics both in the original space and its dual. In the 3-dimensional case, the lattice consists of tetrahedra and cuboctahedra.

Keywords: billiard; confocal quadrics; discrete integrable systems; double reflection nets

Classification (MSC2000): 37J35;14H70;37D05;51N25

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Electronic fulltext finalized on: 18 Nov 2015. This page was last modified: 6 Jan 2016.

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