Bifurcations in Hamiltonian systems : computing singularities by Gröbner bases
Author(s)
Bibliographic Information
Bifurcations in Hamiltonian systems : computing singularities by Gröbner bases
（Lecture notes in mathematics, 1806）
Springer, c2003
Available at / 76 libraries
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
L/N||LNM||180678800561
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INTERNATIONAL CHRISTIAN UNIVERSITY LIBRARY図
V.1806410.8/L507/v.180605941234,
410.8/L507/v.180605941234 -
Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science図書
DC21:514.74/B7852070584020
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Note
Bibliography: p. [159]-165
Includes index
Description and Table of Contents
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, Groebner basis techniques, are applied. The readership addressed consists of advanced graduate students and researchers in dynamical systems.
Table of Contents
- Introduction.- I. Applications: Methods I: Planar reduction
- Method II: The energy-momentum map.- II. Theory: Birkhoff Normalization
- Singularity Theory
- Groebner bases and Standard bases
- Computing normalizing transformations.- Appendix A.1. Classification of term orders
- Appendix A.2. Proof of Proposition 5.8.- References.- Index.
by "Nielsen BookData"
