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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.

Perturbation (Astronomy) --- Series, Lie. --- Hamiltonian systems. --- resonance hamiltonian methods in celestial mechanics and applications --- Hamiltonian dynamical systems --- Systems, Hamiltonian --- Differentiable dynamical systems --- Lie series --- Functions of complex variables --- Celestial mechanics --- Perturbation (Mathematics) --- Mathematics. --- Astrophysics and Astroparticles. --- Theoretical, Mathematical and Computational Physics. --- Astronomy, Observations and Techniques. --- Applications of Mathematics. --- Math --- Science --- Astrophysics. --- Mathematical physics. --- Observations, Astronomical. --- Astronomy—Observations. --- Applied mathematics. --- Engineering mathematics. --- Engineering --- Engineering analysis --- Mathematical analysis --- Astronomical observations --- Observations, Astronomical --- Physical mathematics --- Physics --- Astronomical physics --- Astronomy --- Cosmic physics --- Mathematics