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Field name	Details
Dewey Class	514.74
Title	Bifurcations in Hamiltonian Systems ([EBook]) : Computing Singularities by Gröbner Bases / by Henk Broer, Igor Hoveijn, Gerton Lunter, Gert Vegter.
Author	Broer, Hendrik Walter , 1950-
Added Personal Name	Hoveijn, Igor author.
	Lunter, Gerton author.
	Vegter, Gert author.
Other name(s)	SpringerLink (Online service)
Publication	Berlin, Heidelberg : Springer , 2003.
Physical Details	XVI, 172 pages : online resource.
Series	Lecture Notes in Mathematics 0075-8434 ; ; 1806
ISBN	9783540363989
Summary Note	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.:
Contents note	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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/b10414
Links to Related Works	Subject References: Computational Science and Engineering . Computer mathematics . Global Analysis and Analysis on Manifolds . Global analysis (Mathematics) . Hamiltonian systems . Manifolds (Mathematics) . Mathematics . Authors: Broer, Hendrik Walter 1950- . Broer, Hendrik Walter, 1950- . Hoveijn, Igor . Lunter, Gerton . Vegter, Gert . Corporate Authors: SpringerLink (Online service) . Series: Lecture Notes in Mathematics . Classification: 514.74 .

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Bifurcations in Hamiltonian Systems: Computing Singularities by Gröbner Bases

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