Closed geodesics and billiards on quadrics related to elliptic KdV solutions

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dc.creatorAbenda, Simonetta
dc.creatorFedorov, Yuri N.
dc.date2004-12-14
dc.date.accessioned2026-07-07T12:46:51Z
dc.date.available2026-07-07T12:46:51Z
dc.descriptionWe consider algebraic geometrical properties of the integrable billiard on a quadric Q with elastic impacts along another quadric confocal to Q. These properties are in sharp contrast with those of the ellipsoidal Birkhoff billiards. Namely, generic complex invariant manifolds are not Abelian varieties, and the billiard map is no more algebraic. A Poncelet-like theorem for such system is known. We give explicit sufficient conditions both for closed geodesics and periodic billiard orbits on Q and discuss their relation with the elliptic KdV solutions and elliptic Calogero system
dc.description23 pages, Latex, 1 figure Postscript
dc.identifierhttps://arxiv.org/abs/nlin/0412034
dc.identifierhttp://arxiv.org/abs/nlin/0412034
dc.identifierLetters in Mathematical Physics (2006) 76:111-134
dc.identifierdoi:10.1007/s11005-006-0065-7
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/221521
dc.subjectExactly Solvable and Integrable Systems
dc.subjectDynamical Systems
dc.titleClosed geodesics and billiards on quadrics related to elliptic KdV solutions
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