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Introduction to the Perturbation Theory of Hamiltonian Systems

  • Dmitry Treschev
  • Oleg Zubelevich

Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages I-X
  2. Dmitry Treschev, Oleg Zubelevich
    Pages 1-21
  3. Dmitry Treschev, Oleg Zubelevich
    Pages 23-58
  4. Dmitry Treschev, Oleg Zubelevich
    Pages 59-74
  5. Dmitry Treschev, Oleg Zubelevich
    Pages 75-92
  6. Dmitry Treschev, Oleg Zubelevich
    Pages 93-106
  7. Dmitry Treschev, Oleg Zubelevich
    Pages 107-130
  8. Dmitry Treschev, Oleg Zubelevich
    Pages 131-142
  9. Dmitry Treschev, Oleg Zubelevich
    Pages 143-162
  10. Dmitry Treschev, Oleg Zubelevich
    Pages 163-200
  11. Back Matter
    Pages 201-211

About this book

Introduction

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.

Keywords

Hamiltonian dynamics KAM theory Kolmogorov–Arnold–Moser theorem dynamics hamiltonian system manifold mechanics perturbation theory

Authors and affiliations

  • Dmitry Treschev
    • 1
  • Oleg Zubelevich
    • 2
  1. 1.Steklov Mathematical Inst., Dept. Theoretical PhysicsRussian Aacademy of SciencesMoscowRussian Federation
  2. 2.Russian Federation, Budget & Treasury AcademyMinistry of Finance of theMoskvaRussian Federation

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-03028-4
  • Copyright Information Springer-Verlag Berlin Heidelberg 2010
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-03027-7
  • Online ISBN 978-3-642-03028-4
  • Series Print ISSN 1439-7382
  • Buy this book on publisher's site