Attractive invariant fiber bundles

International Journal of Phytoremediation

Volumn 86, Issue 6, 2007, Pages 687-722

  Pötzsche, Christian ^a  

^a TECHNICAL UNIVERSITY OF MUNICH   (Germany)

Author keywords

2000 Mathematics Subject Classifications: 37D10; 37B55; 37C60; 39A11; 65M06; 65Q05; Asymptotic phase; Attractive invariant manifold; Discretization; Inertial manifold; Invariant fiber bundles; Nonautonomous

Indexed keywords

EID: 55549127102     PISSN: 15226514     EISSN: 15497879     Source Type: Journal    
DOI: 10.1080/00036810701354987     Document Type: Article

References (30)

1. Aulbach, B. 1998. The fundamental existence theorem on invariant fiber bundles. Journal of Difference Equations and Applications, 3: 501–537.
2. 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.
3. 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.
4. Baris, JS. 1969. Integral manifolds of irregularly perturbed differential systems. Ukranian Mathematical Journal, 20: 379–387.
5. 1 semigroups in Banach spaces. Journal of Differential Equations, 139: 283–318.
6. k centre unstable manifolds. Proceedings of Royal Society of Edinburgh, Section A, 108 (3/4): 303–320.
7. 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.
8. 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.
9. Engel, KJ, and Nagel, R. 2000. “ One-Parameter Semigroups for Linear Evolution Equations ”. In Graduate Texts in Mathematics, Vol. 194, Berlin: Springer.
10. 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.
11. Foias, C, Sell, GR, and Témam, R. 1988. Inertial manifolds for nonlinear evolutionary equations. Journal of Differential Equations, 73 (2): 309–353.
12. Hadamard, J. 1901. Sur l'iteration et les solutions asympotiques des equations differentielles. Bulletin de la Société Mathématique de France, 39: 224–228.
13. Henry, D. 1981. “ Geometric Theory of Semilinear Parabolic Equations ”. In Lecture Notes in Mathematics, Vol. 840, Berlin: Springer.
14. Hirsch, MW, Pugh, CC, and Shub, M. 1981. “ Invariant Manifolds ”. In Lecture Notes in Mathematics, Vol. 583, Berlin: Springer.
15. Iooss, G. 1979. Bifurcation of Maps and Applications, Amsterdam: North-Holland.
16. 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.
17. Jones, DA, and Stuart, AM. 1995. Attractive invariant manifolds under approximation. Inertial manifolds, Journal of Differential Equations, 123: 588–637.
18. Kobayasi, K. 1993/94. Inertial manifolds for discrete approximations of evolution equations: convergence and approximations. Advances in Mathematical Sciences and Applications, 3: 161–189.
19. Kobayasi, K. 1995. Convergence and approximation of inertial manifolds for evolution equations. Differential and Integral Equations, 8: 1117–1134.
20. 1 -approximations of inertial manifolds via finite differences. Proceedings of American Mathematical Society, 127 (4): 1143–1150.
21. Kirchgraber, U, and Stiefel, E. 1978. Methoden der analytischen Störungsrechnung und ihre Anwendungen (in german), Stuttgart: B.G. Teubner.
22. Lewin, L. 1982. Polylogarithms and Associated Functions, New York: North Holland.
23. 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.
24. Perron, O. 1930. Die Stabilitätsfrage bei Differentialgleichungen. Mathematische Zeitschrift, 32: 703–728.
25. Poincaré, H. 1886. Mémoire sur les courbes définie par une équation différentielle, IV. Journal of Mathématiques Pures et Appliquées, 2: 151–217.
26. Pliss, VA. 1964. A reduction principle in the theory of stability of motion (in russian). Izv. Akad. Nauk SSSR Ser. Mat., 28: 1297–1324.
27. Pötzsche, C. 2006. Discrete inertial manifolds (Submitted)
28. Pötzsche, C. 2006. Dissipative delay endomorphisms and asymptotic equivalence (Submitted)
29. m -smoothness of invariant fiber bundles. Topological Methods in Nonlinear Analysis, 24 (1): 107–146.
30. Sell, GR, and You, Y. 2002. “ Dynamics of Evolutionary Equations ”. In Applied Mathematical Sciences, Vol. 143, Berlin: Springer.