Integrable systems in the realm of algebraic geometry
Material type: TextLanguage: ENG Series: Lectures Notes in Mathematics ; Vol. 1638Publication details: Heidelberg: Springer-Verlag Berlin, 2001Edition: 2nd edDescription: x, 256p. : ill, pbk. ; 24cmISBN:- 9783540423379
- 516.35 VAN 23rd
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Books | Vigyanpuri Campus | 516.35 VAN (Browse shelf(Opens below)) | Available | 007254 |
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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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