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dc.contributor.authorAbenda, Simonetta
dc.contributor.authorFedorov, Yuri
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I
dc.description.abstractWe 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 Birkho® billiards in Rn. 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 su±cient 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.rightsAttribution-NonCommercial-NoDerivs 2.5 Spain
dc.subject.lcshHamiltonian dynamical systems
dc.subject.lcshLagrangian functions
dc.subject.lcshHamiltonian systems
dc.subject.lcshDifferentiable dynamical systems
dc.subject.otherelliptic KdV solutions
dc.titleClosed Geodesics and Billiards on Quadrics related to elliptic KdV solutions
dc.subject.lemacHamilton, Sistemes de
dc.subject.lemacLagrange, Funcions de
dc.subject.lemacSistemes dinàmics diferenciables
dc.contributor.groupUniversitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
dc.subject.amsClassificació AMS::37 Dynamical systems and ergodic theory::37J Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems
dc.subject.amsClassificació AMS::14 Algebraic geometry::14H Curves
dc.subject.amsClassificació AMS::37 Dynamical systems and ergodic theory::37D Dynamical systems with hyperbolic behavior
dc.subject.amsClassificació AMS::70 Mechanics of particles and systems::70H Hamiltonian and Lagrangian mechanics
dc.rights.accessOpen Access

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