Abstract
In this paper the threshold to global diffusion of a nonmonotonic map, with quadratic nonlinearity, using a forcing function K sinθ as in the standard map, is analyzed. For low values of the stochastic parameter K the breaking of the last KAM curve is caused by the period-one reconnecting resonance. At higher K secondary resonances play an increasingly important role. Two kinds of KAM curves are studied: those between reconnecting resonances and those outside a reconnecting resonance pair. Using a perturbative Hamiltonian method to determine the resonance width a weak overlap criterion is used to estimate the breaking of the last KAM curve outside of the reconnecting islands. For some values of the parameters a nonintegrable reconnecting threshold is found above the threshold of global diffusion. In this regime the reconnection increases the diffusion coefficient to a value close to the quasilinear value of the standard map.
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