Abstract

The Frobenius-Perron operator describes the evolution of density functions in a dynamical system. Finding the �fixed points of this operator is referred to as the Frobenius-Perron problem. This thesis discusses the inverse Frobenius-Perron problem (IFPP), which seeks the transformation that generates a prescribed invariant probability density. In particular, we present in detail five different ways of solving the IFPP, including approaches using conjugation and differential equation, and two matrix solutions. We also generalize Pingel's method to the case of two-pieces maps.