Pol Vanhaecke

Integrable Systems in the Realm of Algebraic Geometry (eBook, PDF)

• Format: PDF

Produktbeschreibung

This book treats the general theory of Poisson structures and integrable systems on affine varieties in a systematic way. Special attention is drawn to algebraic completely integrable systems. Several integrable systems are constructed and studied in detail and a few applications of integrable systems to algebraic geometry are worked out.In the second edition some of the concepts in Poisson geometry are clarified by introducting Poisson cohomology; the Mumford systems are constructed from the algebra of pseudo-differential operators, which clarifies their origin; a new explanation of the multi Hamiltonian structure of the Mumford systems is given by using the loop algebra of sl(2); and finally Goedesic flow on SO(4) is added to illustrate the linearizatin algorith and to give another application of integrable systems to algebraic geometry. TOC: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);...

---

Dieser Download kann aus rechtlichen Gründen nur mit Rechnungsadresse in A, B, BG, CY, CZ, D, DK, EW, E, FIN, F, GR, HR, H, IRL, I, LT, L, LR, M, NL, PL, P, R, S, SLO, SK ausgeliefert werden.

Produktdetails

• Verlag: Springer Berlin Heidelberg
• Seitenzahl: 264
• Erscheinungstermin: 1. Juli 2003
• Englisch
• ISBN-13: 9783540445760
• Artikelnr.: 53430000

Inhaltsangabe

From the 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 ge odesic flow on SO(4); ...