Overview
- Includes supplementary material: sn.pub/extras
Part of the book series: Lecture Notes in Mathematics (LNM, volume 1806)
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Table of contents (10 chapters)
Keywords
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.
Bibliographic Information
Book Title: Bifurcations in Hamiltonian Systems
Book Subtitle: Computing Singularities by Gröbner Bases
Authors: Henk Broer, Igor Hoveijn, Gerton Lunter, Gert Vegter
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/b10414
Publisher: Springer Berlin, Heidelberg
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eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag Berlin Heidelberg 2003
Softcover ISBN: 978-3-540-00403-5Published: 27 February 2003
eBook ISBN: 978-3-540-36398-9Published: 01 January 2003
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: XVI, 172
Topics: Global Analysis and Analysis on Manifolds, Computational Science and Engineering