@Article{AAMM-3-204, author = {Ding , Jiu and Rhee , Noah H.}, title = {A Maximum Entropy Method Based on Orthogonal Polynomials for Frobenius-Perron Operators}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2011}, volume = {3}, number = {2}, pages = {204--218}, abstract = {

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. 

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.10-m1022}, url = {http://global-sci.org/intro/article_detail/aamm/165.html} }