Loop groups, discrete versions of some classical integrable systems, and rank 2 extensions. Memoirs of the American Mathematical Society; 479.

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

ISBN 10: 0821825402 / ISBN 13: 9780821825402

Published by Providence, American Mathemat. Soc, 1992

About this Item

Ehem. Bibliotheksexemplar mit Signatur und Stempel. GUTER Zustand, ein paar Gebrauchsspuren. Ex-library with stamp and library-signature. GOOD condition, some traces of use. C-00848 9780821825402 Sprache: Englisch Gewicht in Gramm: 150.

Seller Inventory # 2484687

Bibliographic Details

• Title: Loop groups, discrete versions of some classical integrable systems, and rank 2 extensions. Memoirs of the American Mathematical Society; 479.
• Publisher: Providence, American Mathemat. Soc
• Publication Date: 1992
• Language: English
• ISBN 10: 0821825402
• ISBN 13: 9780821825402
• Binding: Softcover
• Weight: 150 grams
• Seller catalogs:
  • SA MATHEMATIK

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.