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abstract: 'We use a recently found parametrization of the solutions of the inverse Frobenius-Perron problem within the class of complete unimodal maps to develop a Monte-Carlo approach for the construction of one-dimensional chaotic dynamical laws with given statistical properties, i.e. invariant density and autocorrelation function. A variety of different examples are presented to demonstrate the power of our method.'
author:
- |
    F.K. Diakonos\
    Department of Physics, University of Athens\
    GR-15771, Athens, Greece\
    D.Pingel and P.Schmelcher\
    Theoretische Chemie, Physikalisch–Chemisches Institut\
    Universität Heidelberg, INF 229, D-69120 Heidelberg\
    Federal Republic of Germany
title: '**[A Stochastic Approach to the Construction of One-Dimensional Chaotic Maps with Prescribed Statistical Properties]{}**'
---

Introduction
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Chaotic dynamical systems show a rich diversity of possible behaviour with respect to their statistical properties. In recent years much work has been devoted to the understanding of how these statistical properties emerge from the dynamics. The most popular area for such investigations are unimodal 1-d maps [@Col80; @DynSta; @Gros87; @Cso93]. They became widespread due to two main advantages: their dynamics can be calculated efficiently enough to make extensive numerical investigations and the variety of statistical properties within this class of dynamical laws is very large. Certain features of special systems 