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