A new approach to solving the inverse Frobenius-Perron problem

This paper proposes a new matrix method to solve the inverse problem for the Frobenius-Perron equation. The method can be used to construct a piecewise linear Markov transformation, which approximates the evolution of an unknown dynamical system, based on a sequence of observed probability density functions generated by the system. This particular nonlinear system identification problem is solved using a three-step approach which involves determining the Markov partition, the matrix representation of the Frobenius-Perron operator and finally the corresponding point transformation. A numerical example is used to demonstrate the applicability of the approach.