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020 _a9783540363989
_9978-3-540-36398-9
024 7 _a10.1007/b10414
_2doi
050 4 _aQA614-614.97
072 7 _aPBKS
_2bicssc
072 7 _aMAT034000
_2bisacsh
072 7 _aPBKS
_2thema
082 0 4 _a514.74
_223
100 1 _aBroer, Henk.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aBifurcations in Hamiltonian Systems
_h[electronic resource] :
_bComputing Singularities by Gröbner Bases /
_cby Henk Broer, Igor Hoveijn, Gerton Lunter, Gert Vegter.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2003.
300 _aXVI, 172 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1806
505 0 _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.
650 0 _aGlobal analysis.
650 0 _aComputer science.
650 1 4 _aGlobal Analysis and Analysis on Manifolds.
_0http://scigraph.springernature.com/things/product-market-codes/M12082
650 2 4 _aComputational Science and Engineering.
_0http://scigraph.springernature.com/things/product-market-codes/M14026
700 1 _aHoveijn, Igor.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
700 1 _aLunter, Gerton.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
700 1 _aVegter, Gert.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783540004035
776 0 8 _iPrinted edition:
_z9783662193358
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1806
856 4 0 _uhttps://doi.org/10.1007/b10414
912 _aZDB-2-SMA
912 _aZDB-2-LNM
912 _aZDB-2-BAE
999 _c10399
_d10399