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OverviewThis 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. Full Product DetailsAuthor: Pol VanhaeckePublisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K Edition: 2nd ed. 2001 Volume: 1638 Dimensions: Width: 15.50cm , Height: 1.40cm , Length: 23.50cm Weight: 0.860kg ISBN: 9783540423379ISBN 10: 3540423370 Pages: 264 Publication Date: 31 July 2001 Audience: College/higher education , Professional and scholarly , Undergraduate , Postgraduate, Research & Scholarly Format: Paperback Publisher's Status: Active Availability: Awaiting stock  The supplier is currently out of stock of this item. It will be ordered for you and placed on backorder. Once it does come back in stock, we will ship it out for you. Table of ContentsI. Introduction: II. Integrable Hamiltonian systems on affine Poisson varieties: 1. Introduction.- 2. Affine Poisson varieties and their morphisms.- 3. Integrable Hamiltonian systems and their morphisms.- 4. Integrable Hamiltonian systems on other spaces.- III. Integrable Hamiltonian systems and symmetric products of curves: 1. Introduction.- 2. The systems and their integrability.- 3. The geometry of the level manifolds.- IV. Interludium: the geometry of Abelian varieties 1. Introduction.- 2. Divisors and line bundles.- 3. Abelian varieties.- 4. Jacobi varieties.- 5. Abelian surfaces of type (1,4).- V. Algebraic completely integrable Hamiltonian systems: 1. Introduction.- 2. A.c.i. systems.- 3. Painlev analysis for a.c.i. systems.- 4. The linearization of two-dimensional a.c.i. systems.- 5. Lax equations.- VI. The Mumford systems 1. Introduction.- 2. Genesis.- 3. Multi-Hamiltonian structure and symmetries.- 4. The odd and the even Mumford systems.- 5. The general case.- VII. Two-dimensional a.c.i. systems and applications 1. Introduction.- 2. The genus two Mumford systems.- 3. Application: generalized Kummersurfaces.- 4. The Garnier potential.- 5. An integrable geodesic flow on SO(4).- 6. The Hnon-Heiles hierarchy.- 7. The Toda lattice.- References.- Index.ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
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