Loop Groups, Discrete Versions of Some Classical Integrable Systems, and Rank 2 Extensions (Memoirs of the American Mathematical Society)

Deift, Percy; Li, Luen-Chau; Tomei, Carlos

ISBN 10: 0821825402 / ISBN 13: 9780821825402

Published by Amer Mathematical Society, 1992

About this Item

Good condition. Volume 100, number 479. A copy that has been read but remains intact. May contain markings such as bookplates, stamps, limited notes and highlighting, or a few light stains.

Seller Inventory # V04B-03449

Bibliographic Details

• Title: Loop Groups, Discrete Versions of Some Classical Integrable Systems, and Rank 2 Extensions (Memoirs of the American Mathematical Society)
• Publisher: Amer Mathematical Society
• Publication Date: 1992
• Language: English
• ISBN 10: 0821825402
• ISBN 13: 9780821825402
• Binding: Soft cover
• Condition: Good

About this title

Synopsis

The theory of classical $R$-matrices provides a unified approach to the understanding of most, if not all, known integrable systems. This work, which is suitable as a graduate textbook in the modern theory of integrable systems, presents an exposition of $R$-matrix theory by means of examples, some old, some new. In particular, the authors construct continuous versions of a variety of discrete systems of the type introduced recently by Moser and Vesclov. In the framework the authors establish, these discrete systems appear as time-one maps of integrable Hamiltonian flows on co-adjoint orbits of appropriate loop groups, which are in turn constructed from more primitive loop groups by means of classical $R$-matrix theory. Examples include the discrete Euler-Arnold top and the billiard ball problem in an elliptical region in $n$ dimensions. Earlier results of Moser on rank 2 extensions of a fixed matrix can be incorporated into this framework, which implies in particular that many well-known integrable systems---such as the Neumann system, periodic Toda, geodesic flow on an ellipsoid, etc.---can also be analyzed by this method.