Convergence rates of perturbed attracting sets with vanishing perturbation

Journal of Mathematical Analysis and Applications

Volumn 244, Issue 2, 2000, Pages 369-392

  Grüne, Lars ^a  

^a GOETHE UNIVERSITY   (Germany)

Author keywords

Attracting sets; Numerical approximation; Perturbations; Rate of convergence

Indexed keywords

EID: 0034654717     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmaa.2000.6707     Document Type: Article

References (12)

1. Colonius F., Kliemann W. The Dynamics of Control. 1999;Birkhäuser, Boston.
2. Dellnitz M., Hohmann A. A subdivision algorithm for the computation of unstable manifolds and global attractors. Numer. Math. 75:1997;293-317.
3. Eden A., Foias C., Nicolaenko B., Temam R. Exponential attractors for dissipative evolution equations. Research in Applied Mathematics. 37:1994;Wiley, New York.
4. Fiedler B., Scheurle J. Discretization of homoclinic orbits, rapid forcing and "invisible" chaos. Mem. Amer. Math. Soc. 570:1996.
5. Grüne L., Sontag E. D., Wirth F. R. Asymptotic stability equals exponential stability, and ISS equals finite energy gain - if you twist your eyes. Syst. Control Lett. 38:1999;127-134.
6. Häckl G. Reachable sets, control sets and their computation. Augsburger Mathematisch-Naturwissenschaftliche Schriften. 7:1995;Wißner Verlag, Augsburg.
7. Hale J. K. Asymptotic behavior of dissipative systems. Mathematical Surveys and Monographs. 25:1988;American Mathematical Society, Providence.
8. Kloeden P. E., Keller H., Schmalfuss B. Towards a theory of random numerical dynamics. Crauel H., Gundlach M. Stochastic Dynamics. 1999;259-282 Springer-Verlag, Berlin, New York.
9. P. E. Kloeden, and, V. S. Kozyakin, The inflation of attractors and their discretization, Preprint 22/99, DFG-Schwerpunktprogramm "Dynamik: Analysis, effiziente Simulation und Ergodentheorie,", 1999.
10. Kloeden P. E., Lorenz J. Stable attracting sets in dynamical systems and their one-step discretizations. SIAM J. Numer. Anal. 23:1986;986-995.
11. Stuart A. M., Humphries A. R. Dynamical Systems and Numerical Analysis. 1996;Cambridge Univ. Press, Cambridge.
12. Zou Y.-K., Beyn W.-J. Invariant manifolds for nonautonomous systems with application to one-step methods. J. Dyn. Differential Equations. 10:1997;379-407.