Differentiability of the diffusion coefficient for a family of intermittent maps

Abstract

It is well known that the Liverani-Saussol-Vaienti map satisfies a central limit theorem for Hölder observables in the parameter regime where the correlations are summable. We show that when C 2 observables are considered, the variance of the limiting normal distribution is a C 1 function of the parameter. We first show this for the first return map to the base of the second branch by studying the Green-Kubo formula, then conclude the result for the original map using Kac's lemma and relying on linear response.