  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.
