  The Pomeau-Manneville map is a paradigmatic intermittent dynamical system
exhibiting weak chaos and anomalous dynamics. In this paper we analyse the
parameter dependence of superdiffusion for the map lifted periodically onto the
real line. From numerical simulations we compute the generalised diffusion
coefficient (GDC) of this model as a function of the map's nonlinearity
parameter. We identify two singular dynamical transitions in the GDC, one where
it diverges to infinity, and a second one where it is fully suppressed. Using
the continuous-time random walk theory of L\'evy walks we calculate an analytic
expression for the GDC and show that it qualitatively reproduces these two
transitions. Quantitatively it systematically deviates from the deterministic
dynamics for small parameter values, which we explain by slow decay of velocity
correlations. Interestingly, imposing aging onto the dynamics in simulations
eliminates the dynamical transition that led to suppression of the GDC, thus
yielding a non-trivial change in the parameter dependence of superdiffusion.
This also applies to a respective intermittent model of subdiffusive dynamics
displaying a related transition.
