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

Editore: Providence, American Mathemat. Soc, 1992

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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.

Codice articolo 2484687

Dati bibliografici

• Titolo: Loop groups, discrete versions of some classical integrable systems, and rank 2 extensions. Memoirs of the American Mathematical Society; 479.
• Editore: Providence, American Mathemat. Soc
• Data di pubblicazione: 1992
• Lingua: Inglese
• ISBN 10: 0821825402
• ISBN 13: 9780821825402
• Rilegatura: Softcover
• Peso: 150 grammi
• Cataloghi dei venditori:
  • SA MATHEMATIK

Descrizione articolo

Riassunto

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 analysed by this method.

Contenuti

Introduction; The discrete Euler-Arnold equation (I); The discrete Euler-Arnold equation (II); Billiards in an elliptical region; Loop groups and rank 2 extensions; Appendix: Classical R-matrix theory.