Slow and fast variables in non-autonomous difference equations

Journal of Difference Equations and Applications

Volumn 9, Issue 5, 2003, Pages 473-487

  Pötzsche, Christian ^a  

^a UNIVERSITY OF AUGSBURG   (Germany)

Author keywords

Dichotomy; Invariant manifolds; Singularly perturbed systems

Indexed keywords

EID: 0037572321     PISSN: 10236198     EISSN: None     Source Type: Journal    
DOI: 10.1080/1023619031000076542     Document Type: Article

References (22)

1. R. H. Abraham, J. E. Marsden and T. Ratiu, Manifolds, Tensor Analysis, and Applications, Applied Mathematical Sciences, Vol. 75, Springer-Verlag, Berlin, 1998.
2. R. P. Agarwal, Difference Equations and Inequalities, Marcel Dekker, New York, 1992.
3. J. S. Baris, Integral manifolds of irregularly perturbed differential systems (in Russian), Ukrainiskii Matematikicheskii Žurnal, 20 (1968), 439-448.
4. C. Comstock and G. C. Hsiao, Singular perturbations for difference equations, Rocky Mountain Journal of Mathematics, 6(4) (1976), 561-567.
5. W. A. Coppel, Dichotomies in Stability Theory, Lecture Notes in Mathematics, Vol. 629, Springer-Verlag, Berlin, 1978.
6. N. Fenichel, Persistence and smoothness of invariant manifolds for flows, Indiana University Mathematics Journal, 21 (1971), 193-226.
7. N. Fenichel, Geometric singular perturbation theory for ordinary differential equations, Journal of Differential Equations, 31 (1979), 53-98.
8. D. Henry, Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Mathematics, Vol. 840, Springer-Verlag, Berlin, 1980.
9. W. G. Kelley, Singularly perturbed difference equations, Journal of Difference Equations and Applications, 5 (1999), 97-110.
10. S. Lang, Real and Functional Analysis, Graduate Texts in Mathematics, Vol. 142, Springer-Verlag, Berlin, 1993.
11. K. Nipp, Invariant manifolds of singularly perturbed ordinary differential equations, Journal of Applied Mathematics and Physics (ZAMP), 36 (1985), 309-320.
12. K. Nipp, Smooth attractive invariant manifolds of singularly perturbed ODE's, Research Report No. 92-13, Seminar für Angewandte Mathematik, ETH Zürich, 1992.
13. K. Nipp and D. Stoffer, Invariant manifolds and global error estimates of numerical integration schemes applied to stiff systems of singular perturbation type - Part I: RK-methods, Numerische Mathematik (Electronic Edition), 70 (1995), 245-257.
14. C. Pötzsche, Slow Fiber Bundles of Dynamic Equations on Measure Chains (in German), Logos-Verlag, Berlin, 2002.
15. K. P. Rybakowski, On proving existence and smoothness of invariant manifolds in singular perturbation problem, Topological Methods in Nonlinear Analysis, Journal of the Juliusz Schauder Center, 2 (1993), 21-34.
16. R. J. Sacker and G. R. Sell, A spectral theory for linear differential systems, Journal of Differential Equations, 27 (1978), 320-358.
17. R. J. Sacker and G. R. Sell, Singular Perturbations and Conditional Stability, Journal of Mathematical Analysis and Applications, 76(2) (1980), 406-431.
18. Sakamoto, K. (1990) Invariant manifolds in singular perturbation problems for ordinary differential equations, Proceedings of the Royal Society Edinburgh, Section A 116, No. 1/2, pp. 45-78.
19. K. Sakamoto, Estimates on the strength of exponential dichotomies and application to integral manifolds, Journal of Differential Equations, 107 (1994), 259-279.
20. M. Stiefenhofer, Singular perturbations with limit points in the fast dynamics, Zeitschrift für angewandte Mathematik und Physik, 49 (1998), 730-758.
21. M. Suzuki, Singular perturbation for difference equations, Nonlinear Analysis, Theory, Methods and Applications, 47 (2001), 4083-4093.
22. K. V. Zadiraka, On a nonlocal integral manifold of a nonregularly perturbed differential system (in Russian), Ukrainiskii Matematikicheskii Žurnal, 17 (1965), 47-63.