Computing the diffusion coefficient for intermittent maps: Resummation of stability ordered cycle expansions

Abstract

We compute the diffusion coefficient and the Lyapunov exponent for a diffusive intermittent map by means of cycle expansion of dynamical zeta functions. The asymptotic power law decay of the coefficients of the relevant power series is known analytically. This information is used to resum these power series into generalized power series around the algebraic branch point whose immediate vicinity determines the desired quantities. In particular, we consider a realistic situation where all orbits with instability up to a certain cutoff are known. This implies that only a few of the power series coefficients are known exactly, and many of them are only approximately given. We develop methods to extract information from these stability ordered cycle expansions, and compute accurate values for the diffusion coefficient and the Lyapunov exponent. The method works successfully all the way up to a phase transition of the map, beyond which the diffusion coefficient and Lyapunov exponent are both zero.