000 | 03210nam a22004935i 4500 | ||
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001 | 978-3-319-10777-6 | ||
003 | DE-He213 | ||
005 | 20190213151738.0 | ||
007 | cr nn 008mamaa | ||
008 | 141108s2015 gw | s |||| 0|eng d | ||
020 |
_a9783319107776 _9978-3-319-10777-6 |
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024 | 7 |
_a10.1007/978-3-319-10777-6 _2doi |
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050 | 4 | _aQA372 | |
072 | 7 |
_aPBKJ _2bicssc |
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072 | 7 |
_aMAT007000 _2bisacsh |
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072 | 7 |
_aPBKJ _2thema |
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082 | 0 | 4 |
_a515.352 _223 |
100 | 1 |
_aLiebscher, Stefan. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut |
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245 | 1 | 0 |
_aBifurcation without Parameters _h[electronic resource] / _cby Stefan Liebscher. |
264 | 1 |
_aCham : _bSpringer International Publishing : _bImprint: Springer, _c2015. |
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300 |
_aXII, 142 p. 34 illus., 29 illus. in color. _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 |
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490 | 1 |
_aLecture Notes in Mathematics, _x0075-8434 ; _v2117 |
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505 | 0 | _aIntroduction -- Methods & Concepts -- Cosymmetries -- Codimension One -- Transcritical Bifurcation -- Poincar´e-Andronov-Hopf Bifurcation -- Application: Decoupling in Networks -- Application: Oscillatory Profiles -- Codimension Two -- egenerate Transcritical Bifurcation -- egenerate Andronov-Hopf Bifurcation -- Bogdanov-Takens Bifurcation -- Zero-Hopf Bifurcation -- Double-Hopf Bifurcation -- Application: Cosmological Models -- Application: Planar Fluid Flow -- Beyond Codimension Two -- Codimension-One Manifolds of Equilibria -- Summary & Outlook. | |
520 | _aTargeted at mathematicians having at least a basic familiarity with classical bifurcation theory, this monograph provides a systematic classification and analysis of bifurcations without parameters in dynamical systems. Although the methods and concepts are briefly introduced, a prior knowledge of center-manifold reductions and normal-form calculations will help the reader to appreciate the presentation. Bifurcations without parameters occur along manifolds of equilibria, at points where normal hyperbolicity of the manifold is violated. The general theory, illustrated by many applications, aims at a geometric understanding of the local dynamics near the bifurcation points. | ||
650 | 0 | _aDifferential Equations. | |
650 | 0 | _aDifferential equations, partial. | |
650 | 0 | _aDifferentiable dynamical systems. | |
650 | 1 | 4 |
_aOrdinary Differential Equations. _0http://scigraph.springernature.com/things/product-market-codes/M12147 |
650 | 2 | 4 |
_aPartial Differential Equations. _0http://scigraph.springernature.com/things/product-market-codes/M12155 |
650 | 2 | 4 |
_aDynamical Systems and Ergodic Theory. _0http://scigraph.springernature.com/things/product-market-codes/M1204X |
710 | 2 | _aSpringerLink (Online service) | |
773 | 0 | _tSpringer eBooks | |
776 | 0 | 8 |
_iPrinted edition: _z9783319107783 |
776 | 0 | 8 |
_iPrinted edition: _z9783319107769 |
830 | 0 |
_aLecture Notes in Mathematics, _x0075-8434 ; _v2117 |
|
856 | 4 | 0 | _uhttps://doi.org/10.1007/978-3-319-10777-6 |
912 | _aZDB-2-SMA | ||
912 | _aZDB-2-LNM | ||
999 |
_c11737 _d11737 |