Bifurcations in Hamiltonian systems : computing singularities by Gröbner bases
著者
書誌事項
Bifurcations in Hamiltonian systems : computing singularities by Gröbner bases
（Lecture notes in mathematics, 1806）
Springer, c2003
大学図書館所蔵 件 / 全76件
-
該当する所蔵館はありません
- すべての絞り込み条件を解除する
注記
Bibliography: p. [159]-165
Includes index
内容説明・目次
内容説明
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.
目次
- 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.
「Nielsen BookData」 より