Large-scale chaos for arbitrarily small perturbations in non-twist Hamiltonian systems

The overlapping of isochronous resonances of non-twist Hamiltonian systems can be studied by considering integrable models which result in a smooth reconnection of the homoclinic and heteroclinic manifolds. A complex net of separatrices is formed that depends on the number of the overlapped resonances and their characteristic type. One degree of freedom Hamiltonians are constructed that can describe efficiently the topological structure of non-twist systems. Applying the Melnivovʹs method, it is shown that, for arbitrarily small perturbations, the manifolds intersect transversely and chaotic behaviour spreads on the whole domain of the reconnected separatrices.