|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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