Integrable billiards and quadrics

V. Dragović   ; M. Radnović

Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 65 (2010) no. 2, pp. 319-379

Résumé

Billiards inside quadrics are considered as integrable dynamical systems with a rich geometric structure. The two-way interaction between the dynamics of billiards and the geometry of pencils of quadrics in an arbitrary dimension is considered. Several well-known classical and modern genus-1 results are generalized to arbitrary dimension and genus, such as: the Poncelet theorem, the Darboux theorem, the Weyr theorem, and the Griffiths–Harris space theorem. A synthetic approach to higher-genera addition theorems is presented. Bibliography: 77 titles.

Détail

Keywords: hyperelliptic curve, Jacobian variety, periodic trajectories, Poncelet–Darboux grids, addition theorems.
Mots-clés : Poncelet porism

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