Probability density function over the Lorenz attractor: An alternative foiinulation

Abstract

A new method is proposed to evaluate the probability density function p over the Lorenz attractor. The conservation statement within the continuity equation for p is equivalently replaced by the requirement that all elements of an infinite set of integrals involving p are equal. Two approximations for p are constructed, after considering a finite number s of such integrals and a function II depending upon a set of parameters. The values these parameters assume in the approximation for p are given by the solution of a system of equations which arises from the requirement that the elements of the subset of s integrals are equal. The results are compared with the probability density function coming from the numerical integration of the continuity equation for p.