the autocorrelation function. It is based on the general representation of solutions of the IFPP found in [@PiSchmeDia] for complete smooth unimodal maps. We suitably parametrize the key function $h_f$ occurring in this approach and develop a stochastic (Monte-Carlo) algorithm to determine the optimal solution such that the $\chi^2$ deviation of the resulting autocorrelation from a desired function is minimized. The paper is organized as follows: In section 2 we briefly review the representation of our solution to the IFPP. In section 3 we present the Monte-Carlo algorithm used to perform the $\chi^2$ minimization with respect to the time autocorrelation function. Finally in section 4 we provide several applications in the framework of our Monte-Carlo scheme and discuss the convergence properties of our approach.

The general solution of the IFPP for smooth unimodal 1-d maps
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In a recent paper [@PiSchmeDia] we investigated the problem of designing dynamical systems which possess an arbitrary but fixed invariant density. The solution to this inverse problem is of great interest for the numerical simulation of real physical systems as well as for the understanding of the relationship between the functional form of the map and the statistical features of the corresponding dynamics. We 