Canonical Perturbation Theories, Degenerate Systems and Resonance presents the foundations of Hamiltonian Perturbation Theories used in Celestial Mechanics, emphasizing the Lie Series Theory and its application to degenerate systems and resonance.

This book is the complete text on the subject including advanced topics in Hamiltonian Mechanics, Hori's Theory, and the classical theories of Poincaré, von Zeipel-Brouwer, and Delaunay. Also covered are Kolmogorov's frequency relocation method to avoid small divisors, the construction of action-angle variables for integrable systems, and a complete overview of some problems in Classical Mechanics.

Sylvio Ferraz-Mello makes these ideas accessible not only to Astronomers, but also to those in the related fields of Physics and Mathematics.

Résumé

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.

Contenu
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.