Mathematical Physics III - Integrable Systems of Classical Mechanics: Lecture Notes (Paperback) (ISBN-13: 9783832539504)

These Lecture Notes provide an introduction to the modern theory of classical finite-dimensional integrable systems. The first chapter focuses on some classical topics of differential geometry. This should help the reader to get acquainted with the required language of smooth manifolds, Lie groups and Lie algebras. The second chapter is devoted to Poisson and symplectic geometry with special emphasis on the construction of finite-dimensional Hamiltonian systems. Multi-Hamiltonian systems are also considered. In the third chapter the classical theory of Arnold-Liouville integrability is presented, while chapter four is devoted to a general overview of the modern theory of integrability. Among the topics covered are: Lie-Poisson structures, Lax formalism, double Lie algebras, R-brackets, Adler-Kostant-Symes scheme, Lie bialgebras, r-brackets. Some examples (Toda system, Garnier system, Gaudin system, Lagrange top) are presented in chapter five. They provide a concrete illustration of the theoretical part. Finally, the last chapter is devoted to a short overview of the problem of integrable discretization.

Author: Matteo Petrera
ISBN-10: 3832539506
ISBN-13: 9783832539504
Publisher: Logos Verlag Berlin
Language: English
Published: 05/30/2015
Pages: 190
Format: Paperback
Weight: 0.75lbs
Size: 9.40h x 6.70w x 0.50d