Pullback attractors in nonautonomous difference equations

Journal of Difference Equations and Applications

Volumn 6, Issue 1, 2000, Pages 33-52

  Kloeden, Peter E ^a  

^a GOETHE UNIVERSITY   (Germany)

Author keywords

Cocycle; Difference equation; Pullback attractor

Indexed keywords

EID: 0038229615     PISSN: 10236198     EISSN: 15635120     Source Type: Journal    
DOI: 10.1080/10236190008808212     Document Type: Article

References (19)

1. N. Bhatia and G.P. Szegö, Stability Theory of Dynamicaf Systems. Springer-Veriag, Berlin, 1970.
2. D.N. Cheban, Global attract tors of infinite-dimensional nonautonomous dynamical systems. Izvestiya Akad Nauk RM. Mathematika 25(3) (1997), 42-57.
3. D.N. Cheban, P.E. Kloeden and B. Schmalfubß, Pullback attractors in dissipative nonautonomous differential equations under discretization (submitted).
4. H Crauel and F Randoli, Xitractors for random djjnamical systems, Probab. Theory Relat. Fields 100 (1994), 365-393.
5. P. Diamond and P.E. Kloeden, Spatial discretization of mappings, J. Conzputers Math. Applns. 26 (1993), 85-94.
6. F. Flandoli and B. Schmalfubß Random attractors?or fie 3d stochastic Kavier Stokes equation with mdtiplicative white naise, Stochatics and Stochastic Reports 59 (1996),21-45.
7. J Elale, Asymptotic behaviour of Dissipative dynamical Systems, Amer. Math. Soc., Providence, RI, 1988.
8. P.E. Kloeden, Lyapunov functions for cocycle attractors in nonautonomous difference equation, Izvestiya Akad Nauk RM. Mathemtika 26 (1998), 32-42.
9. P E. Kloeden, Spatial discretization of pullback attractors of nonautonomous difference equations, in Proceedings of the Fourth International Congress on Doyerence Equarions and Appiicaiions, Porn&, August 1998 (to appear).
10. P.E. Kloeden, H. Keller and B. Schmalfubß, Towards a theory of random numerical dynamics. In Random Dynamical Systems. A Festschrift in Honour of Ludwig Arnold. Editors: F. Colonius, M. Gundlach and W. Kliernann. Springer-Verlag, 1999.
11. P.E. Kloeden and J. Lorenz, Stable attracting sets in dynamical systems and their one-step discretizations, SZAM J. Numer. Anal. 23 (1986), 986-995.
12. P.E. Kloeden and B. Schmalfubß, Lyapunov functions and attractors under variable time-step, discretizations Discrete Conts. Dynamical Systems 2 (1996): 163-172.
13. P.E. Kloeden and B. Schmalfubß. Cocvcle attractors sets of variable time-step discretizations of Lorenzian systems, J. Difference Egns. Applns. 3 (1997).
14. P.E. Kloeden and B. Schmalfubß, Nonautonomous systems, cocycle attractors and variable time-step discretization, Numer. Algorithms 14 (1997), 141-152.
15. P.E. Kloeden and B. Schmalfubß, Asymptotic behaviour of nonautonomous difference inclusions. Systems & Control Letters 33 (1998), 275-280.
16. M.A. Krasnosel'skii, The Operator of Translation along Trajectories of Djfferential Equations, Translations of Mathematical Monographs, Vol. 19. American Math. Soc., Providence R.I., 1968.
17. B. Schmalfubß, The stochastic attractor of the stochastic Lorenz system in Nonlinear Dynamics: Attractor Approximation and Global Behaviour, Proc. ISAM 92 (Editors: N. Koksch, V. Reitrnann and T. Riedrich), TU Dresden, 1992, pp. 185-192.
18. A.M. Stuart and A.R. Humphries, Numerical Analysis and Dynamical Systems, Cambridge University Press, Cambridge 1996.
19. K.S. Sibirsky, Introduction to Topological Dynamics. Noordhoff, Leyden, 1975.