Introduction to the Perturbation Theory of Hamiltonian Systems

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's Formula.

From the reviews:

"This Springer monograph, based on lectures given by the first author at Moscow State University ... regarded as a textbook on 'advanced topics in perturbative Hamiltonian mechanics'. ... The style is concise and precise, and the book is suitable for graduate students and researchers. Proofs are usually complete and, if not, references are given. In conclusion, the book constitutes a precious addition to the literature concerning the dynamics of perturbation theory of Hamiltonian systems." (Luigi Chierchia, Mathematical Reviews, Issue 2011 b)

"The present book is an excellent introduction to this subject and covers several classical topics: the KAM theory (and the Birkhoff theorem); the Poincaré-Melnikov theory of the splitting of asymptotic manifolds (in connection with chaos); the separatrix map (and generalizations). Also, special methods are used: asymptotical formulas describing quantitatively stochastic layers; averaging procedures. ... In conclusion, the book will be a very good reference for beginners." (Mircea Crâsmareanu, Zentralblatt MATH, Vol. 1181, 2010)

"This is a very readable textbook on regular perturbation theory of Hamiltonian systems. ... The appendix on diophantine properties, resonance, etc., and specific functional analytic methods is a very valuable addition rendering the text almost self-contained. Most results are given with complete proofs, so that the book may be of good service to researchers and graduate students with interest in mechanics." (G. Hörmann, Monatshefte für Mathematik, Vol. 162 (2), February, 2011)