Lecture Notes in Mathematics

Bifurcations in Hamiltonian Systems

Computing Singularities by Gröbner Bases

Authors: Broer, H., Hoveijn, I., Lunter, G., Vegter, G.

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About this book

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.

Table of contents (10 chapters)

Buy this book

eBook $34.99
price for USA (gross)
  • ISBN 978-3-540-36398-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $49.95
price for USA
  • ISBN 978-3-540-00403-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Bifurcations in Hamiltonian Systems
Book Subtitle
Computing Singularities by Gröbner Bases
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
1806
Copyright
2003
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-36398-9
DOI
10.1007/b10414
Softcover ISBN
978-3-540-00403-5
Series ISSN
0075-8434
Edition Number
1
Number of Pages
XVI, 172
Topics