Author | Vanhaecke, Pol. author |
---|---|

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 |

CONTENT

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