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  • © 2007

Local and Semi-Local Bifurcations in Hamiltonian Dynamical Systems

Results and Examples

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

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Table of contents (10 chapters)

  1. Front Matter

    Pages I-XV
  2. Introduction

    Pages 1-15
  3. Planar Singularities

    Pages 161-165
  4. Stratifications

    Pages 167-171
  5. Normal Form Theory

    Pages 173-184
  6. Back Matter

    Pages 207-241

About this book

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
  • ordinary differential equations

Reviews

From the reviews:

"This book deals with bifurcations of invariant tori in Hamiltonian systems, in particular in near-integrable systems. … The book closes with a series of appendices, in which technical or more fundamental details are summarised … . This well-written monograph represents a welcome contribution to the literature in this field—I am not aware of a similarly comprehensive and systematic treatment of bifurcations of invariant tori. I recommend the book to any researchers or graduate students working in this field." (Thomas Wagenknecht, Mathematical Reviews, Issue 2008 a)

Authors and Affiliations

  • Mathematisch Instituut, Universiteit Utrecht, TA Utrecht, The Netherlands

    Heinz Hanβmann

Bibliographic Information

Buying options

eBook USD 54.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 69.95
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions