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＜電子ブック＞
Bifurcations in Hamiltonian Systems : Computing Singularities by Gröbner Bases / by Henk Broer, Igor Hoveijn, Gerton Lunter, Gert Vegter
(Lecture Notes in Mathematics. ISSN:16179692 ; 1806)

版	1st ed. 2003.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	2003
大きさ	XVI, 172 p : online resource
著者標目	*Broer, Henk author Hoveijn, Igor author Lunter, Gerton author Vegter, Gert author SpringerLink (Online service)
件　名	LCSH:Global analysis (Mathematics) LCSH:Manifolds (Mathematics) LCSH:Mathematics—Data processing FREE:Global Analysis and Analysis on Manifolds FREE:Computational Science and Engineering
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/b10414

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