Integrable Systems in the Realm of Algebraic (Geometry)

[Prohibitive]

English | 2001 | 236 Pages | ISBN: 3540423370 | PDF | 18 MB

This book treats the general theory of Poisson structures and integrable systems on affine varieties in a systematic way.

English | 2001 | 236 Pages | ISBN: 3540423370 | PDF | 18 MB

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.

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