Title: Integrable systems in the realm of algebraic geometry
First published: 1996
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.
Subjects: Hamiltonian systems, Abelian varieties, Mathematics, Geometry, algebraic, Differentiable dynamical systems, Global analysis (Mathematics), Mathematical physics
LC classification: QA3 .L28 no. 1638, QA564 .L28 no. 1638