Bifurcations in Hamiltonian Systems
Computing Singularities by Gröbner Bases
(Sprache: Englisch)
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...
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Klappentext zu „Bifurcations in Hamiltonian Systems “
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.
Inhaltsverzeichnis zu „Bifurcations in Hamiltonian Systems “
Introduction.- I. Applications: Methods I: Planar reduction; Method II: The energy-momentum map.- II. Theory: Birkhoff Normalization; Singularity Theory; Gröbner bases and Standard bases; Computing normalizing transformations.- Appendix A.1. Classification of term orders; Appendix A.2. Proof of Proposition 5.8.- References.- Index.
Bibliographische Angaben
- Autoren: Henk Broer , Gert Vegter , Gerton Lunter , Igor Hoveijn
- 2003, 2003, 172 Seiten, Maße: 15,5 x 23,5 cm, Kartoniert (TB), Englisch
- By H. Broer, I. Hoveijn, G. Lunter et al.
- Herausgegeben: H. Broer, I. Hoveijn, G. Lunter, G. Vegter
- Verlag: Springer
- ISBN-10: 3540004033
- ISBN-13: 9783540004035
- Erscheinungsdatum: 27.02.2003
Sprache:
Englisch
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