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Loop groups, discrete versions of some classical integrable systems, and rank 2 extensions / Percy Deift, Luen-Chua Li, Carlos Tomei.
- Format:
- Book
- Author/Creator:
- Deift, Percy, 1945- author.
- Series:
- Memoirs of the American Mathematical Society ; Volume 100, Number479.
- Memoirs of the American Mathematical Society, 0065-9266 ; Volume 100, Number 479
- Language:
- English
- Subjects (All):
- Hamiltonian systems.
- Loops (Group theory).
- Physical Description:
- 1 online resource (114 p.)
- Edition:
- 1st ed.
- Place of Publication:
- Providence, Rhode Island, United States : American Mathematical Society, 1992.
- Language Note:
- English
- Summary:
- 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.
- Contents:
- ""Table of Contents""; ""Chapter 1. Introduction""; ""Chapter 2. The discrete Euler-Arnold equation (I)""; ""Chapter 3. The discrete Euler-Arnold equation (II)""; ""Chapter 4. Billiards in an elliptical region""; ""Chapter 5. Loop groups and rank 2 extensions""; ""Appendix. Classical R-matrix theory""; ""Bibliography""
- Notes:
- "November 1992, Volume 100, Number 479 (second of 4 numbers)"--Cover.
- Includes bibliographical references.
- Description based on print version record.
- ISBN:
- 1-4704-0056-1
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