On the scenario of reconnection in non-twist cubic maps

In this paper, we study the reconnection process in the dynamics of cubic non-twist maps, introduced in [Howard JE, Humpherys J. Nonmonotonic twist maps. Physica D 1995; 256–76]. In order to describe the route to reconnection of the involved Poincaré–Birkhoff chains we investigate an approximate interpolating Hamiltonian of the map under study. Our study reveals that the scenario of reconnection of cubic non-twist maps is different from that occurring in the dynamics of quadratic non-twist maps.