A numerical contour dynamics code has been employed to calculate the stable and unstable manifolds related to two interacting magnetic island chains. The magnetic configuration is generated by a nonlinear reconnection process described in D. Borgogno et al. [Phys. Plasmas. 12, 032309 (2005)]. The appearance of the first homoclinic and heteroclinic intersections of the dominant manifolds are shown and one of the associated uniformly hyperbolic orbits is given. The stickiness of the field lines around the island and the eventual development of global stochasticity are discussed. The basic geometry of the magnetic configuration is periodic so that the structure of the manifolds may be compared with the one obtained with Poincaré plots.