# American Institute of Mathematical Sciences

August  2019, 24(8): 3653-3666. doi: 10.3934/dcdsb.2018309

## Invariance principle in the singular perturbations limit

 Department of Mathematics, The Weizmann Institute of Science, Rehovot 7610001, Israel

The paper is dedicated to my friend Peter Kloeden

Received  March 2018 Revised  July 2018 Published  November 2018

We examine the invariance principle in the stability theory of differential equations, within a general singularly perturbed system. The limit dynamics of such a system is depicted by the evolution of a Young measure whose values are invariant measures of the fast equation. We establish an invariance principle for the limit dynamics, and examine the relations, at times subtle, with the singularly perturbed system itself.

Citation: Zvi Artstein. Invariance principle in the singular perturbations limit. Discrete & Continuous Dynamical Systems - B, 2019, 24 (8) : 3653-3666. doi: 10.3934/dcdsb.2018309
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