Lyapunov exponent, generalized entropies and fractal dimensions

Abstract

We calculate the maximal Lyapunov exponent, the generalized entropies, the asymptotic distance between nearby trajectories and the fractal dimensions for a finite two-dimensional system at different initial excitation energies. We show that these quantities have a maximum at about the same excitation energy. The presence of this maximum indicates the transition from a chaotic regime to a more regular one. In the chaotic regime the system is composed mainly of a liquid drop while the regular one corresponds to almost freely flowing particles and small clusters. At the transitional excitation energy the fractal dimensions are similar to those estimated from the Fisher model for a liquid-gas phase transition at the critical point.