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Applicable Analysis
An International Journal
Volume 86, 2007 - Issue 6
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Original Articles

Attractive invariant fiber bundles

Pages 687-722 | Received 29 Dec 2006, Accepted 20 Mar 2007, Published online: 27 Jun 2007

References

  • Aulbach , B . 1998 . The fundamental existence theorem on invariant fiber bundles . Journal of Difference Equations and Applications , 3 : 501 – 537 .
  • Aulbach , B , Pötzsche , C and Siegmund , C . 2002 . A smoothness theorem for invariant fiber bundles . Journal of Dynamics and Differential Equations , 14 ( 3 ) : 519 – 547 .
  • Aulbach , B and Wanner , T . 2003 . Invariant foliations and decoupling of non-autonomous difference equations . Journal of Difference Equations and Applications , 9 ( 5 ) : 459 – 472 .
  • Baris , JS . 1969 . Integral manifolds of irregularly perturbed differential systems . Ukranian Mathematical Journal , 20 : 379 – 387 .
  • Chen , X-Y , Hale , JK and Tan , B . 1997 . Invariant foliations for C 1 semigroups in Banach spaces . Journal of Differential Equations , 139 : 283 – 318 .
  • Chow , S-N and Lu , K . 1988 . C k centre unstable manifolds . Proceedings of Royal Society of Edinburgh, Section A , 108 ( 3/4 ) : 303 – 320 .
  • Demengel , F and Ghidaglia , J-M . 1991 . Intertial manifolds for partial differential evolution equations under time-discretization: existence, convergence, and applications . Journal of Mathematical Analysis and Applications , 155 : 177 – 225 .
  • van Dorsselaer , JLM and Lubich , C . 1999 . Inertial manifolds of parabolic differential equations under higher-order discretizations . IMA Journal of Numerical Analysis , 19 : 455 – 471 .
  • Engel , KJ and Nagel , R . 2000 . “ One-Parameter Semigroups for Linear Evolution Equations ” . In Graduate Texts in Mathematics, Vol. 194 , Berlin : Springer .
  • Eriksson , K and Johnson , C . 2000 . Adaptive finite element methods for parabolic problems IV: nonlinear problems . SIAM Journal of Numerical Analysis , 32 ( 6 ) : 1729 – 1749 .
  • Foias , C , Sell , GR and Témam , R . 1988 . Inertial manifolds for nonlinear evolutionary equations . Journal of Differential Equations , 73 ( 2 ) : 309 – 353 .
  • Hadamard , J . 1901 . Sur l'iteration et les solutions asympotiques des equations differentielles . Bulletin de la Société Mathématique de France , 39 : 224 – 228 .
  • Henry , D . 1981 . “ Geometric Theory of Semilinear Parabolic Equations ” . In Lecture Notes in Mathematics , Vol. 840 , Berlin : Springer .
  • Hirsch , MW , Pugh , CC and Shub , M . 1981 . “ Invariant Manifolds ” . In Lecture Notes in Mathematics , Vol. 583 , Berlin : Springer .
  • Iooss , G . 1979 . Bifurcation of Maps and Applications , Amsterdam : North-Holland .
  • Jones , DA , Stuart , AW and Titi , ES . 1998 . Persistence of invariant sets for dissipative evolution equations . Journal of Mathematical Analysis and Applications , 219 : 479 – 502 .
  • Jones , DA and Stuart , AM . 1995 . Attractive invariant manifolds under approximation . Inertial manifolds, Journal of Differential Equations , 123 : 588 – 637 .
  • Kobayasi , K . 1993/94 . Inertial manifolds for discrete approximations of evolution equations: convergence and approximations . Advances in Mathematical Sciences and Applications , 3 : 161 – 189 .
  • Kobayasi , K . 1995 . Convergence and approximation of inertial manifolds for evolution equations . Differential and Integral Equations , 8 : 1117 – 1134 .
  • Kobayasi , K . 1999 . C 1-approximations of inertial manifolds via finite differences . Proceedings of American Mathematical Society , 127 ( 4 ) : 1143 – 1150 .
  • Kirchgraber , U and Stiefel , E . 1978 . Methoden der analytischen Störungsrechnung und ihre Anwendungen (in german) , Stuttgart : B.G. Teubner .
  • Lewin , L . 1982 . Polylogarithms and Associated Functions , New York : North Holland .
  • Nipp , K and Stoffer , D . 1992 . Attractive invariant manifolds for maps: existence, smoothness and continuous dependence on the map, Research Report No. 92-11 . Seminar für Angewandte Mathematik, ETH Zürich . 1992 .
  • Perron , O . 1930 . Die Stabilitätsfrage bei Differentialgleichungen . Mathematische Zeitschrift , 32 : 703 – 728 .
  • Poincaré , H . 1886 . Mémoire sur les courbes définie par une équation différentielle, IV . Journal of Mathématiques Pures et Appliquées , 2 : 151 – 217 .
  • Pliss , VA . 1964 . A reduction principle in the theory of stability of motion (in russian) . Izv. Akad. Nauk SSSR Ser. Mat. , 28 : 1297 – 1324 .
  • Pötzsche , C . 2006 . Discrete inertial manifolds (Submitted)
  • Pötzsche , C . 2006 . Dissipative delay endomorphisms and asymptotic equivalence (Submitted)
  • Pötzsche , C and Siegmund , S . 2004 . C m-smoothness of invariant fiber bundles . Topological Methods in Nonlinear Analysis , 24 ( 1 ) : 107 – 146 .
  • Sell , GR and You , Y . 2002 . “ Dynamics of Evolutionary Equations ” . In Applied Mathematical Sciences , Vol. 143 , Berlin : Springer .

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