Reconnection scenarios and the threshold of reconnection in the dynamics of non-twist maps

Reconnection is a global bifurcation of the invariant manifolds of two or more distinct hyperbolic orbits of a non-twist area preserving map of the annulus, having the same rotation number. We show that for a generic perturbation of an integrable non-twist area preserving map there exist two possible scenarios of reconnection. At the threshold of reconnection the involved hyperbolic orbits are connected. The threshold of reconnection is defined in terms of the action values on the hyperbolic orbits which reconnect, action being a real-valued function constructed from a primitive function of the map.