On singularly perturbed ordinary differential equations with measure-valued limits. (English) Zbl 1016.34057

Artstein, Zvi

Math. Bohem. 127, No. 2, 139-152 (2002).

Summary: The limit behaviour of solutions to 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.

MSC:

34E15	Singular perturbations for ordinary differential equations
34E10	Perturbations, asymptotics of solutions to ordinary differential equations
34D45	Attractors of solutions to ordinary differential equations

Keywords:

singular perturbations; invariant measures; slow and fast motions