Statistical properties of long return times in type I intermittency

We study a class of maps of the unit interval with a neutral fixed point such as those modeling Pomeau-Manneville type 1 intermittency. We construct the invariant ergodic probability measure corresponding to a suitable (expanding) indice version of the original map and use it to prove the same result obtained by Collet, Galves and Schmitt for a piecewise linear model; i.e. that the distribution of the (suitably rescaled) return time in a vanishingly small neighborhood of the indifferent fixed point converges to a mean one exponential law.