Spinning tops : a course on integrable systems
著者
書誌事項
Spinning tops : a course on integrable systems
（Cambridge studies in advanced mathematics, 51）
Cambridge University Press, 1996
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注記
Includes bibliographical references (p. [131]-136) and index
内容説明・目次
内容説明
Since the time of Lagrange and Euler, it has been well known that an understanding of algebraic curves can illuminate the picture of rigid bodies provided by classical mechanics. A modern view of the role played by algebraic geometry has been established iby many mathematicians. This book presents some of these techniques, which fall within the orbit of finite dimensional integrable systems. The main body of the text presents a rich assortment of methods and ideas from algebraic geometry prompted by classical mechanics, whilst in appendices the general, abstract theory is described. The methods are given a topological application to the study of Liouville tori and their bifurcations. The book is based on courses for graduate students given by the author at Strasbourg University but the wealth of original ideas will make it also appeal to researchers.
目次
- Introduction
- 1. The rigid body with a fixed point
- 2. The symmetric spinning top
- 3. The Kowalevski top
- 4. The free rigid body
- 5. Non-compact levels: a Toda lattice
- Appendix 1. A Poisson structure on the dual of a Lie algebra
- Appendix 2. R-matrices and the 'AKS theorem'
- Appendix 3. The eigenvector mapping and linearising flows
- Appendix 4. Complex curves, real curves and their Jacobians
- Appendix 5. Prym varieties
- Bibliography
- Index.
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