Integrable systems in the realm of algebraic geometry

By:

Vanhaecke, Pol

Material type: Text

TextLanguage: ENG Series: Lectures Notes in Mathematics ; Vol. 1638Publication details: Heidelberg: Springer-Verlag Berlin, 2001Edition: 2nd edDescription: x, 256p. : ill, pbk. ; 24cmISBN:

9783540423379

Subject(s):

DDC classification:

516.35 VAN 23rd

Summary: 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. Includes illustrations, bibliographic references and index.

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Holdings
Item type	Current library	Call number	Status	Date due	Barcode
Books	Vigyanpuri Campus	516.35 VAN (Browse shelf(Opens below))	Available		007255
Books	Vigyanpuri Campus	516.35 VAN (Browse shelf(Opens below))	Available		007254

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.

Includes illustrations, bibliographic references and index.

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