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

Authors

Jiu Ding, University of Southern MississippiFollow
Noah H. Rhee, University of Missouri, Kansas CityFollow

Document Type

Article

Publication Date

4-1-2011

Department

Mathematics

School

Mathematics and Natural Sciences

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: L¹ → L¹ 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.

Publication Title

Advances in Applied Mathematics and Mechanics

Volume

3

Issue

2

First Page

204

Last Page

218

Recommended Citation

Ding, J., 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