The power spectrum of geodesic divergences as an early detector of chaoticmotion

We propose a new method for determining the stochastic or ordered nature of trajectories in non-integrable Hamiltonian dynamical systems. The method c onsists in constructing a time-series from the divergence of nearby traject ories and then performing a power spectrum analysis of the series. Ordered trajectories present a spectrum that consists of a few spikes while the spe ctrum of stochastic trajectories is continuous. A test of the method with t hree different systems, a 2-D mapping as well as a 2-D and a 3-D Hamiltonia n, shows that the method is fast and efficient, even in the case of sticky trajectories. The method is also applied to the motion of asteroids in the Solar System.