title: Lyapunov exponents in unstable systems.
abstract: We investigate the dynamical behavior of unstable systems in the vicinity of the critical point associated with a liquid-gas phase transition. By considering a mean-field treatment, we first perform a linear analysis and discuss the instability growth times. Then, coming to complete Vlasov simulations, we investigate the role of nonlinear effects and calculate the Lyapunov exponents. As a main result, we find that near the critical point, the Lyapunov exponents exhibit a power-law behavior, with a critical exponent beta=0.5. This suggests that in thermodynamical systems the Lyapunov exponent behaves as an order parameter to signal the transition from the liquid to the gas phase.
authors.affiliation: Laboratorio Nazionale del Sud, Via S. Sofia 44, I-95123 Catania, Italy.
authors.forename: M
authors.initials: M
authors.lastname: Colonna
authors.forename: A
authors.initials: A
authors.lastname: Bonasera