ENGLISH

Bifurcations in Hamiltonian Systems: Computing Singularities by Gröbner Bases

By Henk Broer , Igor Hoveijn , Gerton Lunter , Gert Vegter (auth.)

Book information

Publisher
Springer-Verlag Berlin Heidelberg
Year
2003
ISBN
3540004033, 9783540004035
DOI
10.1007/b10414
ISSN
0075-8434
Open Library ID
OL17720644M
Language
english
Format
PDF
Filesize
2 MB (1659882 bytes)
Series
Lecture Notes in Mathematics 1806
Edition
1
Pages
172\177
Library
Kolxo3
Scanned
yes
Time added
2009-07-20 03:45:11
Global Analysis and Analysis on Manifolds; Computa

Description

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.

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