dc.contributor.author Fedorov, Yuri dc.contributor.other Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I dc.date.accessioned 2007-10-01T16:03:38Z dc.date.available 2007-10-01T16:03:38Z dc.date.issued 2003 dc.identifier.uri http://hdl.handle.net/2117/1199 dc.description.abstract There exists an in infite hierarchy of integrable generalizations of the geodesic flow on an n -di- mensional ellipsoid.hese generalizations describe the motion of a point in the force fields of certain polynomial potentials.In the limit as one of semiaxes of the ellipsoidtends to zero,one obtains inte- grable mappings corresponding to billiards with polynomial potentials inside an (n+1)-dimensional ellipsoid. In this paper, for the first time we give explicit expressions for the ellipsoidal billiard with a quadratic (Hooke)potential,its representation in Lax form,and a theta function solution.We also indicate the generating function of the restriction of the potential billiard map to a level set of an energy type integral. The methodwe use to obtain theta function solutions is different from those applied earlier and is based on the calculation of limit values of meromorphic functions on generalized Jacobians. dc.format.extent 10 pages dc.language.iso eng dc.rights Attribution-NonCommercial-NoDerivs 2.5 Spain dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/2.5/es/ dc.subject.lcsh Hamiltonian systems dc.subject.lcsh Curves dc.subject.lcsh Hamiltonian dynamical systems dc.subject.lcsh Lagrangian functions dc.subject.other ellipsoidal billiard dc.title An ellipsoidal billiard with a quadratic potential dc.type Article dc.subject.lemac Hamilton, Sistemes de dc.subject.lemac Corbes dc.subject.lemac Lagrange, Funcions de dc.subject.ams Classificació AMS::14 Algebraic geometry::14H Curves dc.subject.ams Classificació AMS::37 Dynamical systems and ergodic theory::37J Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems dc.subject.ams Classificació AMS::70 Mechanics of particles and systems::70H Hamiltonian and Lagrangian mechanics dc.rights.access Open Access
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