The power spectrum of geodesic divergences as an early detector of chaotic motion
Abstract
We propose a new method for determining the stochastic or ordered nature of trajectories in non-integrable Hamiltonian dynamical systems. The method consists in 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.
- Publication:
-
Astronomy and Astrophysics
- Pub Date:
- July 2000
- DOI:
- 10.48550/arXiv.nlin/0005031
- arXiv:
- arXiv:nlin/0005031
- Bibcode:
- 2000A&A...359..386V
- Keywords:
-
- CHAOS;
- METHODS: NUMERICAL;
- CELESTIAL MECHANICS;
- STELLAR DYNAMICS;
- Nonlinear Sciences - Chaotic Dynamics
- E-Print:
- 11 pages, 20 figures, to be published in Astronomy &