Stochasticity of dynamical systems with increasing number of degrees of freedom

Abstract

An isolated one-dimensional self-gravitating system consisting of $N$ plane parallel sheets with uniform density is taken as a model problem for the study of the stochasticity of dynamical systems when the number of degrees of freedom increases. It appears that the proportion of the measure of the "ergodic" domain with respect to the whole volume of the phase space increases very rapidly with the number of degrees of freedom.