Bifurcations in Hamiltonian Systems

Computing Singularities by Gröbner Bases

Henk Broer, Igor Hoveijn, Gerton Lunter , Gert Vegter

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English

Springer-Verlag Berlin and Heidelberg GmbH & Co. K
27 February 2003

Analytic topology; Applied mathematics

Series: Lecture Notes in Mathematics

Summary
Details

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.

By: Henk Broer, Igor Hoveijn, Gerton Lunter, Gert Vegter
Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Country of Publication: Germany
Edition: 2003 ed.
Volume: 1806
Dimensions: Height: 235mm, Width: 155mm, Spine: 10mm
Weight: 600g
ISBN: 9783540004035
ISBN 10: 3540004033
Series: Lecture Notes in Mathematics
Pages: 172
Publication Date: 27 February 2003
Audience: College/higher education , Professional and scholarly , Professional & Vocational , A / AS level , Further / Higher Education
Format: Paperback
Publisher's Status: Active