Dynamical and transport properties in a family of intermittent area-preserving maps

We introduce a family of area-preserving maps representing a (nontrivial) 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.