000 | 03335nam a22005175i 4500 | ||
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001 | 978-3-540-36398-9 | ||
003 | DE-He213 | ||
005 | 20190213151346.0 | ||
007 | cr nn 008mamaa | ||
008 | 121227s2003 gw | s |||| 0|eng d | ||
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. |
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300 |
_aXVI, 172 p. _bonline resource. |
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336 |
_atext _btxt _2rdacontent |
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337 |
_acomputer _bc _2rdamedia |
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338 |
_aonline resource _bcr _2rdacarrier |
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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 |