For the discrete-time quadratic map x t+1 =4x t (1-x t ) the evolution equation for a class of non-uniform initial densities is obtained. It is shown that in the t to infinity limit all of them approach the invariant density for the map.
Dr. V . M. Nandakumaran, “Invariant density for a class of initial distributions under quadratic mapping”, Journal of Physics A: Mathematical and General, vol. 18, p. L1021, 1985.