Integrable Systems in the Realm of Algebraic Geometry (Lecture Notes in Mathematics)

Category	Mathematics
Author	Pol Vanhaecke
Publisher	Springer
Published	2001-09-06
Language	English
ISBN10	3540423370
ISBN13	9783540423379
Tags	algebraic geometry integrable poisson systems
Description	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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