Continuity properties of transport coefficients in simple maps

We consider families of dynamics that can be described in terms of Perron-Frobenius operators with exponential mixing properties. For piecewise C(2) expanding interval maps we rigorously prove continuity properties of the drift J(lambda) and of the diffusion coefficient D(lambda) under parameter variation. Our main result is that D(lambda) has a modulus of continuity of order O(vertical bar delta lambda vertical bar . (log vertical bar delta lambda vertical bar)(2)), i. e. D(lambda) is Lipschitz continuous up to quadratic logarithmic corrections. For a special class of piecewise linear maps we provide more precise estimates at specific parameter values. Our analytical findings are quantified numerically for the latter class of maps by using exact series expansions for the transport coefficients that can be evaluated numerically. We numerically observe strong local variations of all continuity properties.