0 M ay 1 99 5 Universal Behavior Of Lyapunov Exponents In Unstable Systems

We calculate the Lyapunov exponents in a classical molecular dynamics framework. The system is composed of few hundreds particles interacting either through Yukawa (Nuclear) or Slater-Kirkwood (Atomic) forces. The forces are chosen to give an Equation of State that resembles the nuclear and the atomic 4 He Equation Of State respectively near the critical point for liquid-gas phase transition. We find the largest fluctuations for an initial " critical temperature ". The largest Lyapunov exponents λ are always positive and can be very well fitted near this " critical temperature " with a functional form λ ∝ |T − T c | −ω , where the exponent ω = 0.15 is independent of the system and mass number. At smaller temperatures we find that λ ∝ T 0.4498 , a universal behavior characteristic of an order to chaos transition.