Mehr lesen
Klappentext 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. Many mathematicians have established a modern view of the role played by algebraic geometry in recent years. This book presents some of these modern 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! while in appendices the author describes general! abstract theory. She gives the methods a topological application! for the first time in book form! to the study of Liouville tori and their bifurcations. Zusammenfassung The main body of this text is a rich assortment of methods and ideas from algebraic geometry prompted by classical mechanics. 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 appeal to researchers also. Inhaltsverzeichnis 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.
