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Local and Semi-Local Bifurcations in Hamiltonian Dynamical Systems

  • Heinz Hanβmann

Part of the Lecture Notes in Mathematics book series (LNM, volume 1893)

Table of contents

  1. Front Matter
    Pages I-XV
  2. Pages 1-15
  3. Pages 161-165
  4. Pages 167-171
  5. Pages 173-184
  6. Back Matter
    Pages 207-241

About this book

Introduction

Once again KAM theory is committed in the context of nearly integrable Hamiltonian systems. While elliptic and hyperbolic tori determine the distribution of maximal invariant tori, they themselves form n-parameter families. Hence, without the need for untypical conditions or external parameters, torus bifurcations of high co-dimension may be found in a single given Hamiltonian system. The text moves gradually from the integrable case, in which symmetries allow for reduction to bifurcating equilibria, to non-integrability, where smooth parametrisations have to be replaced by Cantor sets. Planar singularities and their versal unfoldings are an important ingredient  that helps to explain the underlying dynamics in a transparent way.

Keywords

Cantor Invariant KAM Theory dynamical systems multiparameter bifurcation proof ramified torus bundle symmetry reduction theorem versal unfolding

Authors and affiliations

  • Heinz Hanβmann
    • 1
  1. 1.Mathematisch InstituutUniversiteit UtrechtTA UtrechtThe Netherlands

Bibliographic information

  • DOI https://doi.org/10.1007/3-540-38894-X
  • Copyright Information Springer-Verlag Berlin Heidelberg 2007
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-540-38894-4
  • Online ISBN 978-3-540-38896-8
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site