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We consider families of dynamics that can be described in terms ofPerron-Frobenius operators with exponential mixing properties. For piecewiseC^2 expanding interval maps we rigorously prove continuity properties of thedrift J(l) and of the diffusion coefficient D(l) under parameter variation. Ourmain result is that D(l) has a modulus of continuity of orderO(|dl||log|dl|)^2), i.e. D(l) is Lipschitz continuous up to quadraticlogarithmic corrections. For a special class of piecewise linear maps weprovide more precise estimates at specific parameter values. Our analyticalfindings are verified numerically for the latter class of maps by using exactformulas for the transport coefficients. We numerically observe strong localvariations of all continuity properties.

Continuity properties of transport coefficients in simple maps