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dc.contributor.authorDragović, Vladimiren
dc.contributor.authorRadnović, Milenaen
dc.date.accessioned2020-05-16T17:02:17Z-
dc.date.available2020-05-16T17:02:17Z-
dc.date.issued2006-01-01en
dc.identifier.issn0021-7824en
dc.identifier.urihttp://researchrepository.mi.sanu.ac.rs/handle/123456789/2671-
dc.description.abstractWe 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 proving the effectiveness of the obtained results. We give a thorough analysis of classical ideas and results of Darboux and methodology of Lebesgue; we 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.en
dc.publisherElsevier-
dc.relation.ispartofJournal des Mathematiques Pures et Appliqueesen
dc.subjectPencils of quadrics | Periodic billiard trajectories | Poncelet theoremen
dc.titleGeometry of integrable billiards and pencils of quadricsen
dc.typeArticleen
dc.identifier.doi10.1016/j.matpur.2005.12.002en
dc.identifier.scopus2-s2.0-33744938926en
dc.contributor.affiliationMathematical Institute of the Serbian Academy of Sciences and Arts-
dc.relation.firstpage758en
dc.relation.lastpage790en
dc.relation.issue6en
dc.relation.volume85en
dc.description.rankM21a-
item.cerifentitytypePublications-
item.openairetypeArticle-
item.fulltextNo Fulltext-
item.grantfulltextnone-
item.openairecristypehttp://purl.org/coar/resource_type/c_18cf-
crisitem.author.orcid0000-0002-0295-4743-
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