Invariant probability and entropy measures for multidimensional maps of chaotic attractors

We define and calculate the probability density in phase space and the information entropy of Poincareʹ maps describing the chaotic, stationary behaviour of deterministic dynamical systems with many degrees of freedom. By partitioning the phase space into cells and computing the probability of finding points of the map in each cell, a numeric approximation of the two statistical measures is derived, and the results are applied to study the chaotic dynamics of a system of two coupled nonlinear oscillators.