Integrable Systems of Classical Mechanics and Lie Algebras Volume I

This book offers a systematic presentation of a variety of methods and results concerning integrable systems of classical mechanics.§The investigation of integrable systems was an important line of study in the last century, but up until recently only a small number of examples with two or more degrees of freedom were known. In the last fifteen years however, remarkable progress has been made in this field via the so-called isospectral deformation method which makes extensive use of group-theoretical concepts. The book focuses mainly on the development and applications of this new method, and also gives a fairly complete survey of the older classic results.§Chapter 1 contains the necessary background material and outlines the isospectral deformation method in a Lie-algebraic form.§Chapter 2 gives an account of numerous previously known integrable systems.§Chapter 3 deals with many-body systems of generalized Calogero-Moser type, related to root systems of simple Lie algebras.§Chapter 4 is devoted to the Toda lattice and its various modifications seen from the group-theoretic point of view.§Chapter 5 investigates some additional topics related to many-body systems.§The book will be valuable to students as well as researchers.