Low Frequency Power Spectra and Classification of Hamiltonian Trajectories

Abstract

We consider the problem of trajectory classification (as regular or chaotic) in Hamiltonian systems through power spectrum analysis. We focus our attention on the low frequency domain and we study the asymptotic behavior of the power spectrum when the frequencies tend to zero. A low frequency power estimator γ is derived that indicates the significance of the relative power included by the low frequencies and we show that it is related to the underlying dynamics of the trajectories. The asymptotic behavior of γ along a trajectory is qualitatively similar to that of the finite time Liapunov characteristic number. The standard map is used as a test model, because it is a typical model for describing Hamiltonian dynamics.