2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/144579We 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.9 pages, 11 figuresChaotic Dynamicstext