000 02758nam a22004817a 4500
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
024 7 _a10.2991/978-94-6239-003-4
_2doi
050 4 _aQA313
072 7 _aPBWR
_2bicssc
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.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aAtlantis Series in Dynamical Systems ;
_v2
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
999 _c49121
_d49121