  Measuring the average information that is necessary to describe the behaviour
of a dynamical system leads to a generalization of the Kolmogorov-Sinai
entropy. This is particularly interesting when the system has null entropy and
the information increases less than linearly with respect to time. We consider
two classes of maps of the interval with an indifferent fixed point at the
origin and an infinite natural invariant measure. We calculate that the average
information that is necessary to describe the behaviour of its orbits increases
with time $n$ approximately as $n^\alpha $, where $\alpha<1$ depends only on
the asymptotic behaviour of the map near the origin.
