TY - JOUR T1 - A Maximum Entropy Method Based on Orthogonal Polynomials for Frobenius-Perron Operators AU - Ding , Jiu AU - Rhee , Noah H. JO - Advances in Applied Mathematics and Mechanics VL - 2 SP - 204 EP - 218 PY - 2011 DA - 2011/03 SN - 3 DO - http://doi.org/10.4208/aamm.10-m1022 UR - https://global-sci.org/intro/article_detail/aamm/165.html KW - Frobenius-Perron operator, stationary density, maximum entropy, orthogonal polynomials, Chebyshev polynomials. AB -

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.