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**Session 38 - Modeling & Numerical Methods.**

*Display session, Wednesday, June 11*

*South Main Hall, *

## [38.04] Orbital Complexity, short time Lyapunov exponents and phase space transport in time-independent Hamiltonian Systems

*B. L. Eckstein, H. E. Kandrup, C. Siopis (U. Florida)*
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.

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