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2002, Volume 2, Issue 3: 415-431. Doi: 10.3934/dcdsb.2002.2.415
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Computational information for the logistic map at the chaos threshold

  • 1.

    Department of Mathematics, University of Pisa, via Buonarroti, 2/a, 56127 Pisa

  • 2.

    Centro Interdisciplinare per lo Studio dei Sistemi Complessi, University of Pisa, via Bonanno, 25/b, 56126 Pisa

Received:  July 31, 2001
Revised:  October 31, 2001
Published:  July 2002
Abstract Related Papers Cited by
    Abstract
  • 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.
    Mathematics Subject Classification: 28D20, 37E05, 37M25, 60J10.

    Citation:
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