A piecewise constant method for Frobenius-Perron operators via delta function approximations

Let S:[0,1]→[0,1] be a nonsingular transformation such that the corresponding Frobenius-Perron operator PS:L1(0,1)→L1(0,1) has a stationary density f∗. We develop a piecewise constant method for the numerical computation of f∗, based on the approximation of Dirac's delta function via pulse functions. We show that the numerical scheme out of this new approach is exactly the classic Ulam's method. Numerical results are given for several one dimensional test mappings.