We study the logistic map f(x) = lambdax(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.
|Autori:||BONANNO C; MENCONI G|
|Titolo:||Computational information for the logistic map at the chaos threshold|
|Anno del prodotto:||2002|
|Digital Object Identifier (DOI):||10.3934/dcdsb.2002.2.415|
|Appare nelle tipologie:||1.1 Articolo in rivista|