Noise Scaling of Symbolic Dynamics Entropies

  • James P. Crutchfield
  • Norman H. Packard
Part of the Springer Series in Synergetics book series (SSSYN, volume 17)


An increasing body of experimental evidence supports the belief that random behavior observed in a wide variety of physical systems is due to underlying deterministic dynamics on a low-dimensional chaotic attractor. The behavior exhibited by a chaotic attractor is predictable on short time scales and unpredictable (random) on long time scales. The unpredictability, and so the attractor’s degree of chaos, is effectively measured by the entropy. Symbolic dynamics is the application of information theory to dynamical systems. It provides experimentally applicable techniques to compute the entropy, and also makes precise the difficulty of constructing predictive models of chaotic behavior. Furthermore, symbolic dynamics offers methods to distinguish the features of different kinds of randomness that may be simultaneously present in any data set: chaotic dynamics, noise in the measurement process, and fluctuations in the environment.


Critical Exponent Chaotic Attractor Topological Entropy Symbolic Dynamic Symbol Sequence 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1982

Authors and Affiliations

  • James P. Crutchfield
    • 1
  • Norman H. Packard
    • 1
  1. 1.Physics Board of StudiesUniversity of CaliforniaSanta CruzUSA

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