Labyrinthic standard non-twist map
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We introduce the labyrinthic standard non-twist map, which is a modified non-twist standard map with an additional perturbation which is a period multiple of the original perturbation period. In phase space this map can present several sets of invariant meandering curves due to the reconnection process of isochrones resonances. Inside each meander set we can find a non-twist invariant curve called the shearless curve, with an extreme rotation number, which generates a wide stickiness effect in phase space when it is broken. The birth/break of these shearless curves, as well as their effects on the dynamical transport are studied, showing the formation of many transport barriers in the system.