A drastic facilitation of the onset of global chaos in periodically driven Hamiltonian systems possessing more than one separatrix

Abstract

Shows that there are certain frequencies of the driving force at which the overlap in energy between different-order resonances and the overlap in the phase space between the resonances of the same order are combined resulting in the onset of global chaos at unusually small amplitudes of the driving force. We demonstrate this in detail for a system with more than one separatrix, since the effect is most pronounced in such systems.