Nontwist Hamiltonian systems have shearless invariant curves that act like barriers in phase space [1, 2]. Recently, secondary shearless curves have also been identified in the phase space of twist maps, in the neighbourhood of peculiar bifurcations of elliptic fixed points . We use Slater’s theorem to develop a qualitative and quantitative numerical approach to determine the breakup of invariant curves in the phase space of area-preserving maps . We also determine the breakup critical parameters, of the shearless curves, with a procedure based on the determinism analysis performed on the recurrence plot of orbits near the critical transition . Finally, we present evidences of transport barriers in plasmas confined in the tokamak TCABR  and in the Texas Helimak .
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