On the spectral analysis of trajectories in near-integrable Hamiltonian systems

Abstract

Spectral properties associated with the deformation of tori and the transition to chaos in near-integrable Hamiltonian systems are studied. Information about the construction of tori is provided by studying the evolution of the integrals of the unperturbed system when a perturbation is added. The authors show that the low band of the power spectrum converges exponentially for regular trajectories but they pass abruptly to 1/f alpha divergence when chaos occurs. These results are valid for systems of two or more degrees of freedom and provide a clear distinction between regular and chaotic motion.