The power spectrum of geodesic divergences as an early detector of chaotic motion

Details The power spectrum of geodesic divergences as an early detector of chaotic motion The power spectrum of geodesic divergences as an early detector of chaotic motion

2000-05-16

arxiv.org/abs/nlin/0005031v1

Nonlinear Sciences

Chaotic Dynamics

11 pages, 20 figures, to be published in Astronomy & Astrophysics (A&A)

Scientific paper

We propose a new method for determining the stochastic or ordered nature of trajectories in non-integrable Hamiltonian dynamical systems. The method consists of constructing a time-series from the divergence of nearby trajectories and then performing a power spectrum analysis of the series. Ordered trajectories present a spectrum that consists of a few spikes while the spectrum of stochastic trajectories is continuous. A test of the method with three different systems, a 2-D mapping as well as a 2-D and a 3-D Hamiltonian, 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.

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