Geometry of Integrable Billiards and Pencils of Quadrics

Simple item page
dc.creatorDragovic, Vladimir
dc.creatorRadnovic, Milena
dc.date2005-12-15
dc.date2007-01-06
dc.date.accessioned2026-07-07T07:38:40Z
dc.date.available2026-07-07T07:38:40Z
dc.descriptionWe study the deep interplay between geometry of quadrics in d-dimensional space and the dynamics of related integrable billiard systems. Various generalizations of Poncelet theorem are reviewed. The corresponding analytic conditions of Cayley's type are derived giving the full description of periodical billiard trajectories; among other cases, we consider billiards in arbitrary dimension d with the boundary consisting of arbitrary number k of confocal quadrics. Several important examples are presented in full details demonstrating the effectiveness of the obtained results. We give a thorough analysis of classical ideas and results of Darboux and methodology of Lebesgue, and prove their natural generalizations, obtaining new interesting properties of pencils of quadrics. At the same time, we show essential connections between these classical ideas and the modern algebro-geometric approach in the integrable systems theory.
dc.description49 pages, 14 figures
dc.identifierhttps://arxiv.org/abs/math-ph/0512049
dc.identifierhttp://arxiv.org/abs/math-ph/0512049
dc.identifierJ. Math. Pures Appl. (9) 85 (2006), no. 6, 758--790
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/121172
dc.subjectMathematical Physics
dc.subjectAlgebraic Geometry
dc.subject14H70; 51N35; 70H06
dc.titleGeometry of Integrable Billiards and Pencils of Quadrics
dc.typetext

Files

Collections

arXiv