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 He equation of state, respectively, near the critical point for liquid-gas phase transition. The largest Lyapunov exponents l are always positive and can be very well fitted near the “critical temperature” with a functional form l ~ jT 2 Tcj , where the exponent v ­ 0.15 is independent of the system and mass number. At smaller temperatures we find that l ~ T 0.4498, a universal behavior characteristic of an order to chaos transition.