title: Capturing correlations in chaotic diffusion by approximation methods.
abstract: We investigate three different methods for systematically approximating the diffusion coefficient of a deterministic random walk on the line that contains dynamical correlations that change irregularly under parameter variation. Capturing these correlations by incorporating higher-order terms, all schemes converge to the analytically exact result. Two of these methods are based on expanding the Taylor-Green-Kubo formula for diffusion, while the third method approximates Markov partitions and transition matrices by using a slight variation of the escape rate theory of chaotic diffusion. We check the practicability of the different methods by working them out analytically and numerically for a simple one-dimensional map, study their convergence, and critically discuss their usefulness in identifying a possible fractal instability of parameter-dependent diffusion, in the case of dynamics where exact results for the diffusion coefficient are not available.
authors.affiliation: School of Mathematical Sciences, Queen Mary University of London, Mile End Road, London E1 4NS, UK. g.knight@qmul.ac.uk
authors.forename: Georgie
authors.initials: G
authors.lastname: Knight
authors.forename: Rainer
authors.initials: R
authors.lastname: Klages