Time-averaged coarse variables for multiscale dynamics

(to appear in Quarterly of Applied Mathematics)

by Marshall Slemrod and Amit Acharya

Given an autonomous system of Ordinary Diff erential Equations without an a priori split into slow and fast components, we defi ne a strategy for producing a large class of `slow' variables (constants of fast motion) in a precise sense. The equation of evolution of any such slow variable is deduced. The strategy is to rewrite our system on an in finite dimensional "history" Hilbert space X and defi ne our coarse observation as a functional on X.