## Chaos, complexity, and short time Lyapunov exponents: two alternative characterisations of chaotic orbit segments
^{1} Department of Astronomy, University of Florida,
Gainesville, FL 32611, USA^{2} Department of Physics and Institute for Fundamental
Theory, University of Florida, Gainesville, FL 32611, USA^{3} Department of Mathematics, University of New Mexico,
Albuquerque, NM 87131, USA (kandrup@astro.ufl.edu; eck@astro.ufl.edu;
brendan@math.unm.edu)
This paper compares two tools useful in characterising ensembles of
chaotic orbit segments in a time-independent galactic potential,
namely Fourier spectra and short time Lyapunov exponents. Motivated by
the observation that nearly regular orbit segments have simpler
spectra than do wildly chaotic segments, the
## Contents- 1. Introduction and motivation
- 2. The invariant spectrum of chaos
- 3. The complexity of chaotic orbit segments
- 4. Correlations between complexity and exponential instability
- Acknowledgements
- References
© European Southern Observatory (ESO) 1997 Online publication: July 3, 1998 |