000 | 02758nam a22004817a 4500 | ||
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001 | sulb-eb0027029 | ||
003 | BD-SySUS | ||
005 | 20160413122724.0 | ||
007 | cr nn 008mamaa | ||
008 | 130817s2013 fr | s |||| 0|eng d | ||
020 |
_a9789462390034 _9978-94-6239-003-4 |
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024 | 7 |
_a10.2991/978-94-6239-003-4 _2doi |
|
050 | 4 | _aQA313 | |
072 | 7 |
_aPBWR _2bicssc |
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072 | 7 |
_aMAT034000 _2bisacsh |
|
082 | 0 | 4 |
_a515.39 _223 |
082 | 0 | 4 |
_a515.48 _223 |
100 | 1 |
_aEldering, Jaap. _eauthor. |
|
245 | 1 | 0 |
_aNormally Hyperbolic Invariant Manifolds _h[electronic resource] : _bThe Noncompact Case / _cby Jaap Eldering. |
264 | 1 |
_aParis : _bAtlantis Press : _bImprint: Atlantis Press, _c2013. |
|
300 |
_aXII, 189 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 |
_aAtlantis Series in Dynamical Systems ; _v2 |
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505 | 0 | _aIntroduction -- Manifolds of bounded geometry -- Persistence of noncompact NHIMs -- Extension of results. | |
520 | _aThis monograph treats normally hyperbolic invariant manifolds, with a focus on noncompactness. These objects generalize hyperbolic fixed points and are ubiquitous in dynamical systems. First, normally hyperbolic invariant manifolds and their relation to hyperbolic fixed points and center manifolds, as well as, overviews of history and methods of proofs are presented. Furthermore, issues (such as uniformity and bounded geometry) arising due to noncompactness are discussed in great detail with examples. The main new result shown is a proof of persistence for noncompact normally hyperbolic invariant manifolds in Riemannian manifolds of bounded geometry. This extends well-known results by Fenichel and Hirsch, Pugh and Shub, and is complementary to noncompactness results in Banach spaces by Bates, Lu and Zeng. Along the way, some new results in bounded geometry are obtained and a framework is developed to analyze ODEs in a differential geometric context. Finally, the main result is extended to time and parameter dependent systems and overflowing invariant manifolds. | ||
650 | 0 | _aMathematics. | |
650 | 0 | _aDynamics. | |
650 | 0 | _aErgodic theory. | |
650 | 1 | 4 | _aMathematics. |
650 | 2 | 4 | _aDynamical Systems and Ergodic Theory. |
650 | 2 | 4 | _aMathematics, general. |
710 | 2 | _aSpringerLink (Online service) | |
773 | 0 | _tSpringer eBooks | |
776 | 0 | 8 |
_iPrinted edition: _z9789462390027 |
830 | 0 |
_aAtlantis Series in Dynamical Systems ; _v2 |
|
856 | 4 | 0 | _uhttp://dx.doi.org/10.2991/978-94-6239-003-4 |
912 | _aZDB-2-SMA | ||
942 |
_2Dewey Decimal Classification _ceBooks |
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999 |
_c49121 _d49121 |