A Maximum Entropy Method Based on Orthogonal Polynomials for Frobenius-Perron Operators

作者：Ding Jiu^*; Rhee Noah H

来源：Advances in Applied Mathematics and Mechanics, 2011, 3(2): 204-218.

DOI：10.4208/aamm.10-m1022

• Frobenius-Perron operator
• stationary density
• maximum entropy
• orthogonal polynomials
• Chebyshev polynomials

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.

• 出版日期2011-4