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.
