Time-evolution of the probability density under the action of a deterministic dynamical system

AbstractIn this paper an analysis of the actions of an abstract dynamical system upon an initial probability measure is proposed. In particular, after a preliminary analysis on the absolute continuity of the probability measure, the conditions of existence of an evolution equation on the jacobian of the transformation from the initial state into the final one are defined and some pertinent numerical procedures, to obtain quantitative results on the basis of the said equation, are also proposed