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Discrete maps have been extensively used to model 2-dimensional chaotictransport in plasmas and fluids. Here we focus on area-preserving mapsdescribing finite Larmor radius (FLR) effects on ${\bf E} \times {\bf B}$chaotic transport in magnetized plasmas with zonal flows perturbed byelectrostatic drift waves. FLR effects are included by gyro-averaging theHamiltonians of the maps which, depending on the zonal flow profile, can havemonotonic or non-monotonic frequencies. In the limit of zero Larmor radius, themonotonic frequency map reduces to the standard Chirikov-Taylor map, and, inthe case of non-monotonic frequency, the map reduces to the standard nontwistmap. We show that in both cases FLR leads to chaos suppression, changes in thestability of fixed points, and robustness of transport barriers. FLR effectsare also responsible for changes in the phase space topology and zonal flowbifurcations. Dynamical systems methods based on recurrence time statistics areused to quantify the dependence on the Larmor radius of the threshold for thedestruction of transport barriers.

Area-preserving maps models of gyro-averaged ${\bf E} \times {\bf B}$ chaotic transport