My new book: G. Sardanashvily, “Handbook of Integrable Hamiltonian Systems” (URSS, 2015) has been published.
This book provides 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, Poincare – Lyapunov – Nekhoroshev, and Mishchenko – Fomenko theorems and their generalizations are present 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
in completely integrable systems is described. The 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 Berry