Lyapunov Exponents and the Natural Invariant Density Determination of Chaotic Maps: An Iterative Maximum Entropy Ansatz
Physics and Astronomy
We apply the maximum entropy principle to construct the natural invariant density and the Lyapunov exponent of one-dimensional chaotic maps. Using a novel function reconstruction technique, that is based on the solution of the Hausdorff moment problem via maximizing Shannon entropy, we estimate the invariant density and the Lyapunov exponent of nonlinear maps in one dimension from a knowledge of finite number of moments. The accuracy and the stability of the algorithm are illustrated by comparing our results to a number of nonlinear maps for which the exact analytical results are available. Furthermore, we also consider a very complex example for which no exact analytical result for the invariant density is available. A comparison of our results to those available in the literature is also discussed.
Journal of Physics A-Mathematical and Theoretical
Mead, L. R.
(2010). Lyapunov Exponents and the Natural Invariant Density Determination of Chaotic Maps: An Iterative Maximum Entropy Ansatz. Journal of Physics A-Mathematical and Theoretical, 43(12).
Available at: http://aquila.usm.edu/fac_pubs/764