Shearless bifurcations for two isochronous resonant perturbations

In nontwist systems, primary shearless curves act as barriers to chaotic transport. Surprisingly, the onset of secondary shearless curves has been reported in a few twist systems. Meanwhile, we found that, in twist systems, the onset of these secondary shearless curves is a standard process that may appear as control parameters are varied in situations where there is resonant mode coupling. Namely, we analyze these shearless bifurcations in two-harmonic systems for the standard map, the Ullmann map, and for the Walker-Ford Hamiltonian flow. The onset of shearless curves is related to bifurcations of periodic points. Furthermore, depending on the bifurcation, these shearless curves can emerge alone or in pairs, and in some cases, deform into separatrices.