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

  • Jiu Ding (a1) and Noah H. Rhee (a2)


Let S: [0, 1]→[0, 1] be a chaotic map and let f* be a stationary density of the Frobenius-Perron operator PS : L 1L 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.


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