Integrable billiards and quadrics

被引：14
|
作者：
Dragovic, V. [1 ,2 ]
Radnovic, M. [1 ]
机构：
[1] Math Inst SANU, Belgrade, Serbia
[2] Univ Lisbon, Math Phys Grp, P-1699 Lisbon, Portugal
来源：
RUSSIAN MATHEMATICAL SURVEYS | 2010年 / 65卷 / 02期
关键词：
hyperelliptic curve; Jacobian variety; Poncelet porism; periodic trajectories; Poncelet-Darboux grids; addition theorems; INVARIANT-MEASURES; PONCELET THEOREM; SYSTEMS; BIFURCATIONS; GEODESICS; SURFACES; PENCILS; MODULI;
D O I：
10.1070/RM2010v065n02ABEH004673
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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 Ponce let theorem, the Darboux theorem, the Weyr theorem, and the Griffiths-Harris space theorem. A synthetic approach to higher-genera addition theorems is presented.
引用
收藏
页码：319 / 379
页数：61
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