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.
Author(s): Dmitry Treschev, Oleg Zubelevich (auth.)
Series: Springer Monographs in Mathematics
Edition: 1
Publisher: Springer-Verlag Berlin Heidelberg
Year: 2010
Language: English
Pages: 211
Tags: Dynamical Systems and Ergodic Theory;Analysis;Topology;Mechanics
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
