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AuthorVanhaecke, Pol. author
TitleIntegrable Systems in the realm of Algebraic Geometry [electronic resource] / by Pol Vanhaecke
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg, 2001
Edition Second Edition
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Descript XII, 264 p. online resource


Introduction -- Integrable Hamiltonian systems on affine Poisson varietie: Affine Poisson varieties and their morphisms; Integrable Hamiltonian systems and their morphisms; Integrable Hamiltonian systems on other spaces -- Integrable Hamiltonian systems and symmetric products of curves: The systems and their integrability; The geometry of the level manifolds -- Interludium: the geometry of Abelian varieties: Divisors and line bundles; Abelian varieties; Jacobi varieties; Abelian surfaces of type (1,4) -- Algebraic completely integrable Hamiltonian systems: A.c.i. systems; Painlev analysis for a.c.i. systems; The linearization of two-dimensional a.c.i. systems; Lax equations -- The Mumford systems: Genesis; Multi-Hamiltonian structure and symmetries; The odd and the even Mumford systems; The general case -- Two-dimensional a.c.i. systems and applications: The genus two Mumford systems; Application: generalized Kummersurfaces; The Garnier potential; An integrable geodesic flow on SO(4);..

Mathematics Algebraic geometry Dynamics Ergodic theory Global analysis (Mathematics) Manifolds (Mathematics) Physics Mathematics Dynamical Systems and Ergodic Theory Global Analysis and Analysis on Manifolds Algebraic Geometry Theoretical Mathematical and Computational Physics


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