M.: Krasand, 2015. — 240 p.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 quantum Hamiltonian mechanics. For the convenience of the reader, a number of relevant mathematical topics are compiled in Appendixes.Introduction.
Non-autonomous mechanics.
Hamiltonian mechanics.
Partially integrable systems.
Superintegrable systems.
Superintegrable Kepler system.
Integrable non-autonomous systems.
Quantum superintegrable systems.
Mechanics with time-dependent parameters.
Appendixes.
Bibliography.
Index.
