Canonical Perturbation Theories

Degenerate Systems and Resonance

  • Sylvio Ferraz-Mello

Part of the Astrophysics and Space Science Library book series (ASSL, volume 345)

Table of contents

  1. Front Matter
    Pages I-XIV
  2. Pages 99-125
  3. Pages 127-138
  4. Pages 231-261
  5. Back Matter
    Pages 262-341

About this book


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.


Celestial mechanics Hamiltonian Lie-series theories Mechanics Nonlinear Resonances

Authors and affiliations

  • Sylvio Ferraz-Mello
    • 1
  1. 1.Instituto de Astronomia, Geofísicae e Ciências AtmosféricasUniversidade de São PauloSão PauloBrasil

Bibliographic information