MATHEMATICA BOHEMICA, Vol. 127, No. 2, pp. 139-152 (2002)

On singularly perturbed ordinary differential equations with measure-valued limits

Zvi Artstein

Zvi Artstein, Department of Mathematics, The Weizmann Institute of Science, Rehovot 76100, Israel, e-mail: zvi.artstein@weizmann.ac.il

Abstract: The limit behaviour of solutions of a singularly perturbed system is examined in the case where the fast flow need not converge to a stationary point. The topological convergence as well as information about the distribution of the values of the solutions can be determined in the case that the support of the limit invariant measure of the fast flow is an asymptotically stable attractor.

Keywords: singular perturbations, invariant measures, slow and fast motions

Classification (MSC2000): 34E15, 34D15

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