Integrable Systems in the Realm of Algebraic Geometry

• Main Author: Vanhaecke, Pol (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2001.
• Edition: 2nd ed. 2001.
• Series: Lecture Notes in Mathematics, 1638
• Subjects: Dynamics.; Ergodic theory.; Global analysis (Mathematics).; Manifolds (Mathematics).; Algebraic geometry.; Mathematical physics.; Dynamical Systems and Ergodic Theory.; Global Analysis and Analysis on Manifolds.; Algebraic Geometry.; Theoretical, Mathematical and Computational Physics.

Table of Contents:

• 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);...