Ferraz-Mello S. Canonical Perturbation Theories: Degenerate Systems and Resonance

Springer Science+Business Media, 2007, 341 pagesAstrophysics and Space Science LibraryThe book is written mainly to advanced graduate and post-graduate students following courses in Perturbation Theory and Celestial Mechanics. It is also intended to serve as a guide in research work and is written in a very explicit way: all perturbation theories are given with details allowing its immediate application to real problems. In addition, they are followed by examples showing all steps of their application. The book is not intended to explore the mathematics of Hamiltonian Systems, but may be useful to mathematicians in a great deal of circumstances as a reference on the practical application of the theories. In the same way, it may be a source book on the problems of degeneracy and small divisors, which affect the use of perturbation theories as well in Celestial Mechanics as in Physics.The Hamilton–Jacobi Theory
Angle–Action Variables. Separable Systems
Classical Perturbation Theories
Resonance
Lie Mappings
Lie Series Perturbation Theory
Non-Singular Canonical Variables
Lie Series Theory for Resonant Systems
Single Resonance near a Singularity
Nonlinear Oscillators