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arXiv · 1508.01027

Integrable lattices of hyperplanes related to billiards within confocal quadrics

Milena Radnovic
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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.

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Milena Radnovic. 2015-08-05. Integrable lattices of hyperplanes related to billiards within confocal quadrics. https://arxiv.org/abs/1508.01027

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