Author | Vanhaecke, Pol. author |
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Title | Integrable Systems in the realm of Algebraic Geometry [electronic resource] / by Pol Vanhaecke |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 2001 |
Edition | Second Edition |
Connect to | http://dx.doi.org/10.1007/3-540-44576-5 |
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);..