We discuss homogenization (convergence to a stochastic differential equation) for fast-slow systems where the fast dynamics is given by a 'chaotic' map. David Kelly and Ian Melbourne showed that homogenization follows from certain statistical properties for the fast dynamics, including an enhanced version of the (functional) central limit theorem. These statistical properties have been verified for a wide class of nonuniformly hyperbolic maps, e.g. Anosov diffeomorphisms and Pomeau-Manneville maps.
In this talk, we will give an elementary sufficient condition for deterministic homogenization. We will also present some examples for which it was not previously possible to prove homogenization.