Integrable Systems in the Realm of Algebraic Geometry

von Pol Vanhaecke

276 Seiten, Taschenbuch

Kurzbeschreibung des Verlags

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);...

• Reihe: Lecture Notes in Mathematics
• Themen: Mathematik und Naturwissenschaften Physik Mathematische / Computergestützte / Theoretische Physik
• ISBN: 9783540423379
• Sprache: Englisch
• Erscheinungsdatum: 31.07.2001
• Größe: 233 x 155 mm
• Verlag: Springer