(untitled) (Advances in Applied Mathematics and Mechanics, 2018)
Let S: [0, 1]→[0, 1] be a chaotic map and let f^∗ be a stationary density of the Frobenius-Perron operator P_S: L^1→L^1 associated with S. We develop a numerical algorithm for approximating f^∗, using the maximum entropy approach to an under-determined moment problem and the Chebyshev polynomials for the stability consideration. Numerical experiments show considerable improvements to both the original maximum entropy method and the discrete maximum entropy method.