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Bifurcations in Hamiltonian Systems

Computing Singularities by Gröbner Bases

  • Authors
  • Henk Broer
  • Igor Hoveijn
  • Gerton Lunter
  • Gert Vegter

Part of the Lecture Notes in Mathematics book series (LNM, volume 1806)

Table of contents

  1. Front Matter
    Pages I-XIII
  2. Henk Broer, Igor Hoveijn, Gerton Lunter, Gert Vegter
    Pages 1-18
  3. Henk Broer, Igor Hoveijn, Gerton Lunter, Gert Vegter
    Pages 21-44
  4. Henk Broer, Igor Hoveijn, Gerton Lunter, Gert Vegter
    Pages 45-68
  5. Henk Broer, Igor Hoveijn, Gerton Lunter, Gert Vegter
    Pages 71-84
  6. Henk Broer, Igor Hoveijn, Gerton Lunter, Gert Vegter
    Pages 85-96
  7. Henk Broer, Igor Hoveijn, Gerton Lunter, Gert Vegter
    Pages 97-132
  8. Henk Broer, Igor Hoveijn, Gerton Lunter, Gert Vegter
    Pages 133-151
  9. Henk Broer, Igor Hoveijn, Gerton Lunter, Gert Vegter
    Pages 153-158
  10. Henk Broer, Igor Hoveijn, Gerton Lunter, Gert Vegter
    Pages 159-165
  11. Henk Broer, Igor Hoveijn, Gerton Lunter, Gert Vegter
    Pages 167-169
  12. Back Matter
    Pages 171-171

About this book

Introduction

The authors consider applications of singularity theory and computer algebra to bifurcations of Hamiltonian dynamical systems. They restrict themselves to the case were the following simplification is possible. Near the equilibrium or (quasi-) periodic solution under consideration the linear part allows approximation by a normalized Hamiltonian system with a torus symmetry. It is assumed that reduction by this symmetry leads to a system with one degree of freedom. The volume focuses on two such reduction methods, the planar reduction (or polar coordinates) method and the reduction by the energy momentum mapping. The one-degree-of-freedom system then is tackled by singularity theory, where computer algebra, in particular, Gröbner basis techniques, are applied. The readership addressed consists of advanced graduate students and researchers in dynamical systems.

Keywords

Approximation Gröbner basis computer algebra energy momentum map reduction planar reduction singularity theory symmetry

Bibliographic information

  • DOI https://doi.org/10.1007/b10414
  • Copyright Information Springer-Verlag Berlin Heidelberg 2003
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-00403-5
  • Online ISBN 978-3-540-36398-9
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site