Higher correlation functions of chaotic dynamical systems-a graph theoretical approach

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Abstract
For dynamical systems conjugated to the Bernoulli shift and their higher-dimensional extensions of Kaplan-Yorke type the author calculates higher-order correlation functions by means of a graph theoretical method. The graphs relevant to this problem are forests of incomplete double binary trees. His method has similarities with the Feynman graph approach in quantum field theory: the 'free field' corresponds to a Gaussian random dynamics, the 'interacting field' to a chaotic process with non-trivial higher-order correlations. The 'coupling constant' tau 1/2 is a time scale parameter that measures how much the chaotic process differs from a Gaussian process. He develops a perturbation theory around the Gaussian limit case for sums of iterates of the fully developed logistic map with arbitrary coefficients.

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