Integrable Systems in the Realm of Algebraic Geometry: 1638 (Lecture Notes in Mathematics, 1638) - Softcover

Vanhaecke, Pol

 
9783540423379: Integrable Systems in the Realm of Algebraic Geometry: 1638 (Lecture Notes in Mathematics, 1638)
Softcover
ISBN 10: 3540423370 ISBN 13: 9783540423379
Publisher: Springer, 2001

Synopsis

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.

"synopsis" may belong to another edition of this title.

Synopsis

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 introducing 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, the Goedesic flow on SO(4) is added to illustrate the linearization algorithm and to give another application of integrable systems to algebraic geometry.

"About this title" may belong to another edition of this title.

Publisher
Springer
Publication date
2001
Language
English
ISBN 10 
3540423370
ISBN 13 
9783540423379
Binding
Paperback
Edition number
2
Number of pages
276