Deterministic homogenization for fast–slow systems with chaotic noise

By David Kelly, Ian Melbourne. 2014

84 citations recorded by the source corpus.

Consider a fast-slow system of ordinary differential equations of the form x˙=a(x,y)+e−1b(x,y), y˙=e−2g(y), where it is assumed that b averages to zero under the fast flow generated by g. We give conditions under which solutions x to the slow equations converge weakly to an It\^o diffusion X as e→0. The drift and diffusion coefficients of the limiting stochastic differential equation satisfied by X are given explicitly. Our theory applies when the fast flow is Anosov or Axiom A, as well as to a large class of nonuniformly hyperbolic fast flows (including the one defined by the well-known Lorenz equations), and our main results do not require any mixing assumptions on the fast flow.

Subfields: Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/446b24ae76fb537789f96b9d61f69041ef6d503d

Citations in the corpus

• A Spectral Approach for Quenched Limit Theorems for Random Expanding Dynamical Systems (2017, unknown): “[7,13,23–25,35,42], and another interesting set of related results on limit theorems occur in the setting of homogenisation [22,30,31].”