Buch, Englisch, Band 1806, 172 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 295 g
Reihe: Lecture Notes in Mathematics
Computing Singularities by Gröbner Bases
Buch, Englisch, Band 1806, 172 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 295 g
Reihe: Lecture Notes in Mathematics
ISBN: 978-3-540-00403-5
Verlag: Springer Berlin Heidelberg
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.
Zielgruppe
Research
Autoren/Hrsg.
Fachgebiete
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik
- Mathematik | Informatik Mathematik Topologie Analytische Topologie
- Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik
Weitere Infos & Material
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.
