Integrable Systems in the Realm of Algebraic Geometry

2. Auflage 2001
ISBN: 978-3-540-42337-9
Verlag: Springer

Buch, Englisch, Band 1638, 264 Seiten, Format (B × H): 155 mm x 233 mm, Gewicht: 420 g

Reihe: Lecture Notes in Mathematics

n. 150. 2.4. The KP vector fields. 152. ix 3. Multi-Hamiltonian structure and symmetries. 155. 3.1. The loop algebra 9(q. 155. 3.2. Reducing the R-brackets and the vector field ~. 157. 4. The odd and the even Mumford systems. 161. 4.1. The (odd) Mumford system. 161. 4.2. The even Mumford system. 163.

Zielgruppe

Research

Autoren/Hrsg.

Vanhaecke, Pol

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Mathematische Analysis Integralrechnungen- und -gleichungen

Inhaltsverzeichnis

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);.