Год выпуска: 2015 Автор: Sardanashvily G.A. Издательство: Страниц: ISBN: 978-5-396-00687-4
Описание
This book provides a comprehensive exposition of completely integrable, partially integrable and superintegrable Hamiltonian systems in a general setting of invariant submanifolds which need not be compact. In particular, this is the case of non-autonomous integrable Hamiltonian systems and integrable systems with time-dependent parameters. The fundamental Liouville---Minuer---Arnold, Poincar\'e---Lyapunov---Nekhoroshev, and Mishchenko---Fomenko theorems and their generalizations are presented in details. Global action-angle coordinate systems, including the Kepler one, are analyzed. Geometric quantization of integrable Hamiltonian systems with respect to action-angle variables is developed, and classical and quantum Berry phase phenomenon in completely integrable systems is described. This book addresses to a wide audience of theoreticians and mathematicians of undergraduate, post-graduate and researcher levels. It aims to be a guide to advanced geometric methods in classical and...
