PROBABILITY-DISTRIBUTIONS OF LOCAL LYAPUNOV EXPONENTS FOR HAMILTONIAN-SYSTEMS

We calculate the probability distributions of the largest local Lyapun ov exponent for three Hamiltonian systems at different values of the e nergy E, for a set of increasing values of the length in which the tra jectory is partitioned. The systems we study are the Henon-Heiles mode l and the classical Ar3 and Ar7 clusters. We show that these distribut ions contain much information about the dynamics of the system and, in particular, can be used to study the evolution of ergodic properties as the internal energy of the system increases; therefore, even though the inequivalence of chaos and ergodicity does not allow one to consi der Lyaponov exponents to be a direct measure of ergodicity, the sampl e distributions of short-term Lyapunov exponents can be used to evalua te the extent of ergodic behavior in the various situations.