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
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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)
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1. Introduction
Pages 1-18
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2. Method I: Planar reduction
Pages 21-44
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3. Method II: The energy-momentum map
Pages 45-68
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4. Birkhoff normalization
Pages 71-84
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5. Singularity theory
Pages 85-96
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Table of contents (10 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Bifurcations in Hamiltonian Systems
- Book Subtitle
- Computing Singularities by Gröbner Bases
- Authors
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- Henk Broer
- Igor Hoveijn
- Gerton Lunter
- Gert Vegter
- 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
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