Integrable systems in the realm of algebraic geometry
By: Pol Vanhaecke.
Edition: 2nd ed.
Series: Lecture notes in mathematics,; 1638; Lecture notes in mathematics (Springer-Verlag) ;; 1638.
Publisher: Springer
Published: 2001
Place of publication: Berlin; New York
Language: eng
Number of pages: 256
Subjects: Abelian varieties; Hamiltonian systems
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.
Notes: Includes bibliographical references (p. 243-251) and index.