Introduction to the Perturbation Theory of Hamiltonian Systems

Dmitry Treschev, Oleg Zubelevich (auth.)3642030270, 9783642030277

This book presents the basic methods of regular perturbation theory of Hamiltonian systems, including KAM-theory, splitting of asymptotic manifolds, the separatrix map, averaging, anti-integrable limit, etc. in a readable way. Although concise, it discusses all main aspects of the basic modern theory of perturbed Hamiltonian systems and most results are given with complete proofs.

It will be a valuable reference for Hamiltonian systems, and of special interest to researchers and graduate students of the KAM community.

Table of contents :
Front Matter….Pages I-X
Hamiltonian Equations….Pages 1-21
Introduction to the KAM Theory….Pages 23-58
Splitting of Asymptotic Manifolds….Pages 59-74
The Separatrix Map….Pages 75-92
Width of the Stochastic Layer….Pages 93-106
The Continuous Averaging Method….Pages 107-130
The Anti-Integrable Limit….Pages 131-142
Hill’s Formula….Pages 143-162
Appendix….Pages 163-200
Back Matter….Pages 201-211