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Lecture Notes in Mathematics
cover

Local and Semi-Local Bifurcations in Hamiltonian Dynamical Systems

Results and Examples

Authors: Hanßmann, Heinz

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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.

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)


Table of contents (10 chapters)

Table of contents (10 chapters)
  • Introduction

    Pages 1-15

  • Bifurcations of Equilibria

    Pages 17-89

  • Bifurcations of Periodic Orbits

    Pages 91-107

  • Bifurcations of Invariant Tori

    Pages 109-142

  • Perturbations of Ramified Torus Bundles

    Pages 143-159

Buy this book

eBook $54.99
price for USA in USD
  • ISBN 978-3-540-38896-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $69.95
price for USA in USD
  • ISBN 978-3-540-38894-4
  • with online files
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Local and Semi-Local Bifurcations in Hamiltonian Dynamical Systems
Book Subtitle
Results and Examples
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
1893
Copyright
2007
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-38896-8
DOI
10.1007/3-540-38894-X
Softcover ISBN
978-3-540-38894-4
Series ISSN
0075-8434
Edition Number
1
Number of Pages
XVI, 242
Number of Illustrations
22 b/w illustrations
Topics

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