Universal Behavior of Lyapunov Exponents in Unstable Systems

We calculate the Lyapunov exponents in a classical molecular dynamics framework. Yukawa and Slater-Kirkwood forces are considered in order to give an equation of state that resembles the nuclear and the atomic ⁴He equation of state, respectively, near the critical point for liquid-gas phase transition. The largest Lyapunov exponents λ are always positive and can be very well fitted near the ``critical temperature'' with a functional form λ∝0ex0ex|T-Tc|^-ω, where the exponent ω0ex0ex=0ex0ex0.15 is independent of the system and mass number. At smaller temperatures we find that λ∝T0.4498, a universal behavior characteristic of an order to chaos transition.