Central limit theorem for generalized Weierstrass functions

Let f : S-1 -> S-1 be a C2+epsilon expanding map of the circle and let v : S-1 -> R be a C1+epsilon function. Consider the twisted cohomological equation v = alpha o f -Df . alpha, which has a unique bounded solution alpha. We show that a is either C(1+epsilon )or continuous but nowhere differentiable. If a is nowhere differentiable then the Newton quotients of alpha, after an appropriated normalization, converges in distribution (with respect to the unique absolutely continuous invariant probability of f) to the normal distribution. In particular, alpha is not a Lipschitz continuous function on any subset with positive Lebesgue measure. (AU)