Integrable systems in the realm of algebraic geometry / Pol Vanhaecke.

By: Vanhaecke, Pol, 1963-
Material type: TextTextSeries: Lecture notes in mathematics (Springer-Verlag): 1638.Publisher: Berlin ; New York : Springer-Verlag, ©1996Description: 1 online resource (viii, 218 pages) : illustrationsContent type: text Media type: computer Carrier type: online resourceISBN: 9783662215357; 3662215357Subject(s): Abelian varieties | Hamiltonian systems | Abelian varieties | Hamiltonian systems | Variëteiten van Abel | Algebraische Geometrie | Integrables SystemGenre/Form: Electronic books Additional physical formats: Print version:: Integrable systems in the realm of algebraic geometry.DDC classification: 510 | 516.3/53 LOC classification: QA3 | .L28 no. 1638Other classification: 31.51 Online resources: Click here to access online
Contents:
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.
Action note: digitized 2010 committed to preserveSummary: 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.
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Includes bibliographical references (pages 209-215) and index.

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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.

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.

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