Computational information for the logistic map at the chaos threshold
Claudio Bonanno, Giulia Menconi · Discrete and Continuous Dynamical Systems - B · 2002
We study the logistic map $f(x)=\lambda x (1-x)$ on the unit square atthe chaos threshold. By using the methods of symbolic dynamics, the informationcontent of an orbit of a dynamical system is defined as the AlgorithmicInformation Content (AIC) of a symbolic sequence. We give results for thebehaviour of the AIC for the logistic map. Since the AIC is not a computablefunction we use, as approximation of the AIC, a notion of information contentgiven by the length of the string after it has been compressed by a compressionalgorithm, and in particular we introduce a new compression algorithm calledCASToRe. The information content is then used to characterise the chaoticbehaviour.