Authors: Dragović, Vladimir 
Radnović, Milena
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Integrable billiards and quadrics
Journal: Russian Mathematical Surveys
Volume: 65
Issue: 2
First page: 319
Last page: 379
Issue Date: 1-Nov-2010
Rank: M23
ISSN: 0036-0279
DOI: 10.1070/RM2010v065n02ABEH004673
Abstract: 
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. © 2010 RAS(DoM) and LMS.
Keywords: Addition theorems | Hyperelliptic curve | Jacobian variety | Periodic trajectories | Poncelet porism | Poncelet-Darboux grids
Publisher: Turpion

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