Integrable lattices of hyperplanes related to billiards within confocal quadrics
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Published:2015
Issue:112
Volume:98
Page:25-30
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ISSN:0350-1302
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Container-title:Publications de l'Institut Math?matique (Belgrade)
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language:en
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Short-container-title:Publ Inst Math (Belgr)
Affiliation:
1. Mathematical Institute SANU, Belgrade + University of Sydney, School of Mathematics and Statistics, Sydney, 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.
Funder
Ministry of Education, Science and Technological Development of the Republic of Serbia
Publisher
National Library of Serbia
Subject
General Mathematics