Introduction to the Perturbation Theory of Hamiltonian Systems - Treschev, Dmitry; Zubelevich, Oleg.; SpringerLink (Online service) (Berlin, Heidelberg : Springer Berlin Heidelberg, 2010)
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.
Hamiltonian Equations -- to the KAM Theory -- Splitting of Asymptotic Manifolds -- The Separatrix Map -- Width of the Stochastic Layer -- The Continuous Averaging Method -- The Anti-Integrable Limit -- Hill$1 (Bs Formula.s
Keywords: Mathematics; Global analysis (Mathematics).; Differentiable dynamical systems; Topology; Mechanics; Mathematics; Dynamical Systems and Ergodic Theory; Analysis; Topology; Mechanics