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Computational information for the logistic map at the chaos threshold

Claudio Bonanno·Giulia Menconi
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Abstract

We study the logistic map $f(x)=λx(1-x)$ 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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Claudio Bonanno, Giulia Menconi. 2001-07-24. Computational information for the logistic map at the chaos threshold. https://arxiv.org/abs/nlin/0102034

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