Orbital Complexity, short time Lyapunov exponents and phase space transport in time-independent Hamiltonian Systems
This paper compares two tools useful in characterising ensembles of chaotic orbit segments in a time-independent galactic potential, Fourier spectra and short time Lyapunov exponents. Motivated by the observation that nearly regular orbit segments have simpler spectra then do wildly chaotic segments, the complexity of a discrete Fourier spectrum, defined as the number of frequencies that contain a fraction k of the total power, is identified as a robust quantitative diagnostic in terms of which to classify different chaotic segments. Comparing results derived from such a classification scheme with the computed values of short time Lyapunov exponents shows that there is a strong, nearly linear, correlation between the complexity of an orbit and its sensitive dependence on initial conditions. Chaotic segments characterised by complex Fourier spectra tend systematically to have a larger maximum short time Lyapunov exponent than do segments with simpler spectra. It follows that the distribution of complexities, N[n(k)], associated with an ensemble of chaotic segments of length Delta t can be used as a diagnostic for phase space transport in much the same way as the distribution of maximum Lyapunov exponents, N[chi ], associated with the same ensemble.
American Astronomical Society Meeting Abstracts #190
- Pub Date:
- May 1997