Integrable systems in the realm of algebraic geometry /
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 syste...
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| Format: | eBook |
| Language: | English |
| Published: |
Berlin ; New York :
Springer,
[2001]
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| Edition: | 2nd ed. |
| Series: | Lecture notes in mathematics (Springer-Verlag) ;
1638. |
| Subjects: | |
| Online Access: | Connect to the full text of this electronic book |
| 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. |
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| Item Description: | Electronic resource. |
| Physical Description: | 1 online resource (x, 256 pages) |
| Bibliography: | Includes bibliographical references (pages 243-251) and index. |
| ISBN: | 9783540445760 (electronic bk.) 3540445765 (electronic bk.) |
| ISSN: | 0075-8434 ; |