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
相关论文
共 50 条
  • [1] Geometry of integrable billiards and pencils of quadrics
    Dragovic, Vladimir
    Radnovic, Milena
    JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2006, 85 (06): : 758 - 790
  • [2] INTEGRABLE LATTICES OF HYPERPLANES RELATED TO BILLIARDS WITHIN CONFOCAL QUADRICS
    Radnovic, Milena
    PUBLICATIONS DE L INSTITUT MATHEMATIQUE-BEOGRAD, 2015, 98 (112): : 25 - 30
  • [3] Topological classification of integrable geodesic billiards on quadrics in three-dimensional Euclidean space
    Belozerov, G. V.
    SBORNIK MATHEMATICS, 2020, 211 (11) : 1503 - 1538
  • [4] INTEGRABLE BILLIARDS
    ABDRAHMANOV, AM
    VESTNIK MOSKOVSKOGO UNIVERSITETA SERIYA 1 MATEMATIKA MEKHANIKA, 1990, (06): : 28 - 33
  • [5] Billiards and integrable systems
    Fomenko, A. T.
    Vedyushkina, V. V.
    RUSSIAN MATHEMATICAL SURVEYS, 2023, 78 (05) : 881 - 954
  • [6] INTEGRABLE BIRKHOFF BILLIARDS
    BOLOTIN, SV
    VESTNIK MOSKOVSKOGO UNIVERSITETA SERIYA 1 MATEMATIKA MEKHANIKA, 1990, (02): : 33 - 36
  • [7] INTEGRABLE CURVILINEAR BILLIARDS
    RAMANI, A
    KALLITERAKIS, A
    GRAMMATICOS, B
    DORIZZI, B
    PHYSICS LETTERS A, 1986, 115 (1-2) : 25 - 28
  • [8] Integrable elliptic billiards and ballyards
    Lynch P.
    European Journal of Physics, 2020, 41 (01)
  • [9] Building quasimodes in integrable billiards
    Baldo, M.
    Raciti, F.
    Physics Letters, Section A: General, Atomic and Solid State Physics, 1996, 223 (06): : 417 - 420
  • [10] On algebraically integrable outer billiards
    Tabachnikov, Serge
    PACIFIC JOURNAL OF MATHEMATICS, 2008, 235 (01) : 89 - 92
12345