Integrable systems in the realm of algebraic geometry / Pol Vanhaecke.

Format:

Book

Author/Creator:

Vanhaecke, Pol, 1963-

Series:

Lecture notes in mathematics (Springer-Verlag) ; 1638.

Lecture notes in mathematics, 0075-8434 ; 1638

Language:

English

Subjects (All):

Abelian varieties.

Hamiltonian systems.

Physical Description:

x, 256 pages ; 24 cm.

Edition:

Second edition.

Place of Publication:

Berlin ; New York : Springer, [2001]

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.

Notes:

Includes bibliographical references (pages 243-251) and index.

ISBN:

3540423370

OCLC:

47296301