Integrable systems are related to algebraic geometry in many different ways. This book deals with some aspects of this relation, the main focus being on the algebraic geometry of the level manifolds of integrable systems and the construction of integrable systems, starting from algebraic geometric data. For a rigorous account of these matters, integrable systems are defined on affine algebraic varieties rather than on smooth manifolds. The exposition is self-contained and is accessible at the graduate level; in particular, prior knowledge of integrable systems is not assumed.
Reihe
Sprache
Verlagsort
Verlagsgruppe
Zielgruppe
Für höhere Schule und Studium
Für Beruf und Forschung
Research
Maße
Höhe: 23.5 cm
Breite: 15.5 cm
Gewicht
ISBN-13
978-3-540-61886-7 (9783540618867)
DOI
10.1007/978-3-662-21535-7
Schweitzer Klassifikation
I. Introduction.- II. Integrable Hamiltonian systems on affine Poisson varieties.- III. Integrable Hamiltonian systems and symmetric products of curves.- IV. Interludium: the geometry of Abelian varieties.- V. Algebraic completely integrable Hamiltonian systems.- VI. The master systems.- VII. The Garnier and Hénon-Heiles potentials and the Toda lattice.- References.
