Attractors under perturbation and discretization

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Grüne, Lars:
Attractors under perturbation and discretization.
Bayreuth , 2000

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Abstract

Using control theoretic techniques we give a necessary and sufficient condition for the convergence of attractors in one step discretizations of ordinary differential equations and obtain estimates for the resulting discretization error. The necessary and sufficient condition is based on a robustness property for an associated perturbed system, which is closely related to but slightly weaker than the input-to-state stability property well known in control theory.