Separatrix reconnection and periodic orbit annihilation in the Harper map

Structure of the periodic accelerator orbits of the Harper map is investigated in detail from the view point of underlying scenario of chaos in the area preserving nontwist map. Since the twist function of the Harper map admits rigorous treatment for the entire range of phase variable, the results obtained in the present analysis describes generic novel phenomena, which are outside of the applicability of the Kolmogorov-Arnol'd-Moser theory. (author)