(h, k)-Trichotomies and asymptotics of nonautonomous difference systems

Computers and Mathematics with Applications

Volumn 33, Issue 10, 1997, Pages 105-124

  Lopez Fenner J ^a   Pinto, M ^b  

^a UNIVERSIDAD DE LA FRONTERA   (Chile)

^b UNIVERSITY OF CHILE   (Chile)

Author keywords

Invariant manifolds; Trichotomies; Weakly asymptotically equivalence

Indexed keywords

FINITE DIFFERENCE METHOD; MATHEMATICAL TRANSFORMATIONS;

INVARIANT MANIFOLDS; TRICHOTOMIES; WEAKLY ASYMTOTICALLY EQUIVALENCE;

NONLINEAR SYSTEMS;

EID: 0031128560     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0898-1221(97)00080-1     Document Type: Article

References (17)

1. M. Pinto, Discrete dichotomies, Computers Math. Applic. 28 (1-3), 259-270 (1994).
2. J. Kalkbrenner, Exponentielle Dichotomie und chaotische Dynamik nichtinvertierbarer Differenzengleichungen, Ph.D. Thesis, Universität Augsburg, Augsburg, (July, 1994).
3. B. Aulbach, On linearly perturbed linear systems, Journal of Mathematical Analysis and Its Applications 112, 317-327 (1985).
4. B. Aulbach, Continuous and discrete dynamics near manifolds of equilibria, Lect. Notes in Math. 1058 (1984).
5. H.W. Knobloch and F. Kappel, Gewöhnliche Differentialgleichungen, B.G. Teubner, Stuttgart, (1974).
6. S. Elaydi and O. Hájek, Exponential dichotomy and trichotomy of nonlinear differential equations, Diff. and Int. Equations 3, 1201-1224 (1990).
7. R. Naulín and M. Pinto, Roughness of (h, k)-dichotomies, Journal of Differential Equations 118 (1), 20-35 (1995).
8. M.A. Pinto, Asymptotic integration of a system resulting from the perturbation of an h-system, Journal of Mathematical Analysis and Applications 131 (1), 194-216 (1988).
9. T. Wanner, Zur Linealizierung zufälliger dynamischer Systeme, Ph.D. Thesis, Universität Augsburg, Augsburg, (July, 1993).
10. th International Conference on Differential Equations, Plovdiv, Bulgaria, (1994).
11. D. Henry, Geometric theory of semilinear parabolic equations, Lect. Notes in Math. 840 (1981).
12. K.J. Palmer, Exponential dichotomy, the shadowing lemma and transversal homoclinic points, In Dynamics Reported, (Edited by U. Kirchgraber and H.O. Walter), Volume 1, pp. 265-306, B.G. Teubner, Stuttgart, (1988).
13. B. Aulbach, Invariant manifolds with asymptotic phase, Nonlin. Anal., Theory, Methods and Appl. 6, 817-827 (1982).
14. B. Aulbach, Behavior of solutions near manifolds of periodic solutions, Jour. Diff. Eqs. 39, 345-377 (1981).
15. W.A. Coppel, Dichotomies in stability theory, Lect. Notes in Math., Springer-Verlag 629 (1978).
16. U. Kirchgraber and E. Stiefel, Methoden der analytischen Störungsrechnung und ihre Anwendungen, B.G. Teubner, Stuttgart, (1978).
17. J. López-Fenner and M. Pinto, An integral manifold with bounded projection for nonautonomous, nonlinear systems of (h, k)-hyperbolic type, In Tübinger Berichte zur Funktionalanalysis, Tübingen, (1996).