  We introduce a family of area-preserving maps representing a (non-trivial)
two-dimensional extension of the Pomeau-Manneville family in one dimension. We
analyze the long-time behavior of recurrence time distributions and
correlations, providing analytical and numerical estimates. We study the
transport properties of a suitable lift and use a probabilistic argument to
derive the full spectrum of transport moments. Finally the dynamical effects of
a stochastic perturbation are considered.
