  We consider a general class of maps of the interval having Lyapunov
subexponential instability $|\delta x_{t}|\sim|\delta
x_{0}|\exp[\Lambda_{t}(x_{0})\zeta(t)]$, where $\zeta(t)$ grows sublinearly as
$t\rightarrow\infty$. We outline here a scheme [J. Stat. Phys. {\bf 154}, 988
(2014)] whereby the choice of a characteristic function automatically defines
the map equation and corresponding growth rate $\zeta(t)$. This matching
approach is based on the infinite measure property of such systems. We show
that the average information that is necessary to record without ambiguity a
trajectory of the system tends to $\langle\Lambda\rangle\zeta(t)$, suitably
extending the Kolmogorov-Sinai entropy and Pesin's identity. For such systems,
information behaves like a random variable for random initial conditions, its
statistics obeying a universal Mittag-Leffler law. We show that, for individual
trajectories, information can be accurately inferred by the number of
first-passage times through a given turbulent phase space cell. This enables us
to calculate far more efficiently Lyapunov exponents for such systems. Lastly,
we also show that the usual renewal description of jumps to the turbulent cell,
usually employed in the literature, does not provide the real number of
entrances there. Our results are supported by exhaustive numerical simulations.
