LEADER 03844nam 22006975 450 001 9910144633903321 005 20200706214217.0 010 $a3-540-36398-X 024 7 $a10.1007/b10414 035 $a(CKB)1000000000229450 035 $a(SSID)ssj0000321596 035 $a(PQKBManifestationID)12097329 035 $a(PQKBTitleCode)TC0000321596 035 $a(PQKBWorkID)10280355 035 $a(PQKB)10485670 035 $a(DE-He213)978-3-540-36398-9 035 $a(MiAaPQ)EBC6297390 035 $a(MiAaPQ)EBC5610626 035 $a(Au-PeEL)EBL5610626 035 $a(OCoLC)1078996288 035 $a(PPN)155206494 035 $a(EXLCZ)991000000000229450 100 $a20121227d2003 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aBifurcations in Hamiltonian Systems $eComputing Singularities by Gröbner Bases /$fby Henk Broer, Igor Hoveijn, Gerton Lunter, Gert Vegter 205 $a1st ed. 2003. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2003. 215 $a1 online resource (XVI, 172 p.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1806 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-00403-3 320 $aIncludes bibliographical references (pages [159]-165) and index. 327 $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. 330 $aThe authors consider applications of singularity theory and computer algebra to bifurcations of Hamiltonian dynamical systems. They restrict themselves to the case were the following simplification is possible. Near the equilibrium or (quasi-) periodic solution under consideration the linear part allows approximation by a normalized Hamiltonian system with a torus symmetry. It is assumed that reduction by this symmetry leads to a system with one degree of freedom. The volume focuses on two such reduction methods, the planar reduction (or polar coordinates) method and the reduction by the energy momentum mapping. The one-degree-of-freedom system then is tackled by singularity theory, where computer algebra, in particular, Gröbner basis techniques, are applied. The readership addressed consists of advanced graduate students and researchers in dynamical systems. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v1806 606 $aGlobal analysis (Mathematics) 606 $aManifolds (Mathematics) 606 $aComputer mathematics 606 $aGlobal Analysis and Analysis on Manifolds$3https://scigraph.springernature.com/ontologies/product-market-codes/M12082 606 $aComputational Science and Engineering$3https://scigraph.springernature.com/ontologies/product-market-codes/M14026 615 0$aGlobal analysis (Mathematics). 615 0$aManifolds (Mathematics). 615 0$aComputer mathematics. 615 14$aGlobal Analysis and Analysis on Manifolds. 615 24$aComputational Science and Engineering. 676 $a514.74 700 $aBroer$b Henk$4aut$4http://id.loc.gov/vocabulary/relators/aut$013459 702 $aHoveijn$b Igor$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aLunter$b Gerton$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aVegter$b Gert$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910144633903321 996 $aBifurcations in Hamiltonian systems$9262864 997 $aUNINA