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Integrable lattices of hyperplanes related to billiards within confocal quadrics (1508.01027v1)
Published 5 Aug 2015 in math.DG, math.DS, math.MG, and nlin.SI
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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