Integrable systems in the realm of algebraic geometry /
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 syste...
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| Format: | eBook |
| Language: | English |
| Published: |
Berlin ; New York :
Springer,
[2001]
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| Edition: | 2nd ed. |
| Series: | Lecture notes in mathematics (Springer-Verlag) ;
1638. |
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| Online Access: | Connect to the full text of this electronic book |
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); ...