Computational information for the logistic map at the chaos threshold

Details Computational information for the logistic map at the chaos threshold Computational information for the logistic map at the chaos threshold

2001-02-26

arxiv.org/abs/nlin/0102034v2

Nonlinear Sciences

Chaotic Dynamics

23 pages, 3 figures, changed content

Scientific paper

We study the logistic map $f(x)=\lambda x(1-x)$ on the unit square at the chaos threshold. By using the methods of symbolic dynamics, the information content of an orbit of a dynamical system is defined as the Algorithmic Information Content (AIC) of a symbolic sequence. We give results for the behaviour of the AIC for the logistic map. Since the AIC is not a computable function we use, as approximation of the AIC, a notion of information content given by the length of the string after it has been compressed by a compression algorithm, and in particular we introduce a new compression algorithm called CASToRe. The information content is then used to characterise the chaotic behaviour.

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