The Hamilton Jacobi Theory.- Angle Action Variables.- Jacobian Averaging Theories.- Resonance Delaunay and Bohlin Theories.- Lie Mappings.- Lie Series Averaging Theories.- NonSingular Canonical Variables.- Lie Series Theory for Resonant Systems.- Single Resonance Near A Singularity.- Nonlinear Oscillators.- Appendix.
The 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.
Each theory is presented as a complete recipe which can be followed towards practical application, including warnings against known difficulties
Presents complete solutions and action-angle variables of the elementary integrable systems that serve as starting points in Perturbations Theory
The only book which considers extensively the problem of overcoming the small divisors that appear when Perturbations Theory is used to construct solutions in the neighborhood of a resonance of the proper frequencies