03844nam 22006975 450 991014463390332120200706214217.03-540-36398-X10.1007/b10414(CKB)1000000000229450(SSID)ssj0000321596(PQKBManifestationID)12097329(PQKBTitleCode)TC0000321596(PQKBWorkID)10280355(PQKB)10485670(DE-He213)978-3-540-36398-9(MiAaPQ)EBC6297390(MiAaPQ)EBC5610626(Au-PeEL)EBL5610626(OCoLC)1078996288(PPN)155206494(EXLCZ)99100000000022945020121227d2003 u| 0engurnn|008mamaatxtccrBifurcations in Hamiltonian Systems Computing Singularities by Gröbner Bases /by Henk Broer, Igor Hoveijn, Gerton Lunter, Gert Vegter1st ed. 2003.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,2003.1 online resource (XVI, 172 p.) Lecture Notes in Mathematics,0075-8434 ;1806Bibliographic Level Mode of Issuance: Monograph3-540-00403-3 Includes bibliographical references (pages [159]-165) and index.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.Lecture Notes in Mathematics,0075-8434 ;1806Global analysis (Mathematics)Manifolds (Mathematics)Computer mathematicsGlobal Analysis and Analysis on Manifoldshttps://scigraph.springernature.com/ontologies/product-market-codes/M12082Computational Science and Engineeringhttps://scigraph.springernature.com/ontologies/product-market-codes/M14026Global analysis (Mathematics).Manifolds (Mathematics).Computer mathematics.Global Analysis and Analysis on Manifolds.Computational Science and Engineering.514.74Broer Henkauthttp://id.loc.gov/vocabulary/relators/aut13459Hoveijn Igorauthttp://id.loc.gov/vocabulary/relators/autLunter Gertonauthttp://id.loc.gov/vocabulary/relators/autVegter Gertauthttp://id.loc.gov/vocabulary/relators/autMiAaPQMiAaPQMiAaPQBOOK9910144633903321Bifurcations in Hamiltonian systems262864UNINA