A Maximum Entropy Method Based on Orthogonal Polynomials for Frobenius-Perron Operators (Advances in Applied Mathematics and Mechanics, 2018)
Let $S$: [0, 1]→[0, 1] be a chaotic map and let $f^∗$ be a stationary density ofthe Frobenius-Perron operator $P_S$: $L^1$→$L^1$ associated with $S$. We develop a numericalalgorithm for approximating $f^∗$, using the maximum entropy approach to anunder-determined moment problem and the Chebyshev polynomials for the stabilityconsideration. Numerical experiments show considerable improvements toboth the original maximum entropy method and the discrete maximum entropymethod.