A Maximum Entropy Method Based on Orthogonal Polynomials for Frobenius-Perron Operators
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.
Advances in Applied Mathematics and Mechanics
Rhee, N. H.
(2011). A Maximum Entropy Method Based on Orthogonal Polynomials for Frobenius-Perron Operators. Advances in Applied Mathematics and Mechanics, 3(2), 204-218.
Available at: https://aquila.usm.edu/fac_pubs/376