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Russian Mathematical Surveys, 2010, Volume 65, Issue 2, Pages 319–379
DOI: https://doi.org/10.1070/RM2010v065n02ABEH004673 (Mi rm9349) 		 
This article is cited in 20 scientific papers (total in 20 papers)

Integrable billiards and quadrics

V. Dragovićab, M. Radnovića

a Mathematical Institute SASA, Belgrade, Serbia
b Mathematical Physics Group, University of Lisbon, Portugal
English version PDF (971 kB) Citations (20)
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DOI: https://doi.org/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.
Bibliography: 77 titles.
Keywords: hyperelliptic curve, Jacobian variety, Poncelet porism, periodic trajectories, Poncelet–Darboux grids, addition theorems.
Received: 03.02.2010
Russian version:
Uspekhi Matematicheskikh Nauk, 2010, Volume 65, Issue 2(392), Pages 133–194
DOI: https://doi.org/10.4213/rm9349
Bibliographic databases:
Document Type: Article
UDC: 517.938+531.01
MSC: Primary 37J35, 70J45; Secondary 58E07, 70H06
Language: English
Original paper language: Russian
Citation: V. Dragović, M. Radnović, “Integrable billiards and quadrics”, Uspekhi Mat. Nauk, 65:2(392) (2010), 133–194; Russian Math. Surveys, 65:2 (2010), 319–379
Citation in format AMSBIB
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    • This publication is cited in the following 20 articles:
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    References:96
    First page:39
     
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