## Abstract

We present an unconventional method of estimating all of the Lyapunov
exponents of a dynamical system from either a known map or a set of
experimental data. Rather than averaging exponents along a single
trajectory, we instead represent each exponent as an integral over all
of phase space. The contribution to each exponent, calculated at each
point in phase space, is averaged spatially by weighting areas of high
density more heavily than areas of low density, according to the
invariant measure of the system. Explicit formulae for approximating
both the contributions to the exponents and the invariant measure are
given, and convergence results stated. The techniques are illustrated
in detail for the Henon system.