A novel matrix approach for controlling the invariant densities of chaotic maps

Recent work on positive matrices has resulted in a new matrix method for generating chaotic maps with arbitrary piecewise constant invariant densities, sometimes known as the inverse Frobenius–Perron problem (IFPP). In this paper, we give an extensive introduction to the IFPP, describing existing methods for solving it, and we describe our new matrix approach for solving the IFPP.