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MARC 21

Bifurcations in Hamiltonian Systems: Computing Singularities by Gröbner Bases
Tag	Description
020	$a9783540363989
082	$a514.74
099	$aOnline resource: Springer
100	$aBroer, Hendrik Walter$d1950-
245	$aBifurcations in Hamiltonian Systems$h[EBook]$bComputing Singularities by Gröbner Bases$cby Henk Broer, Igor Hoveijn, Gerton Lunter, Gert Vegter.
260	$aBerlin, Heidelberg$bSpringer$c2003.
300	$aXVI, 172 pages$bonline resource.
336	$atext
338	$aonline resource
440	$aLecture Notes in Mathematics,$x0075-8434 ;$v1806
505	$aIntroduction -- 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.
520	$aThe 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.
538	$aOnline access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
700	$aHoveijn, Igor.$eauthor.
700	$aLunter, Gerton.$eauthor.
700	$aVegter, Gert.$eauthor.
710	$aSpringerLink (Online service)
830	$aLecture Notes in Mathematics,$v1806
856	$uhttp://dx.doi.org/10.1007/b10414