Integrable Systems of Classical Mechanics and Lie Algebras Volume I : Birkhauser : 9783764323363 : 3764323361 : 01 Dec 1989 : This book is designed to expose from a general and universal standpoint a variety ofmethods and results concerning integrable systems ofclassical me­ chanics. By such systems we mean Hamiltonian systems with a finite number of degrees of freedom possessing sufficiently many conserved quantities (in­ tegrals ofmotion) so that in principle integration ofthe correspondingequa­ tions of motion can be reduced to quadratures, i.e. to evaluating integrals of known functions. The investigation of these systems was an important line ofstudy in the last century which, among other things, stimulated the appearance of the theory ofLie groups. Early in our century, however, the work ofH. Poincare made it clear that global integrals of motion for Hamiltonian systems exist only in exceptional cases, and the interest in integrable systems declined. Until recently, only a small