Probability distributions of local Liapunov exponents for small clusters

The probability distribution of the largest local Liapunov exponent is evaluated for a classical ${\mathrm{Ar}}_3$ cluster at different values of the internal energy E, for a set of increasing values of the length in which the trajectory is partitioned. These distributions can be directly related to the evolution of ergodic behavior, particularly to how it exhibits distinctive, separable time scales which depend strongly on the energy of the system. Therefore, even though the inequivalence of ergodicity and chaos prohibits a Liapunov exponent itself from being a quantitative index of ergodicity, we find that 2 the sample distributions used to evaluate Liapunov exponents nevertheless can be used for this purpose.