Journal of Statistical Physics

, Volume 54, Issue 3–4, pp 915–924 | Cite as

Chaotic dynamics, Markov partitions, and Zipf's law

  • G. Nicolis
  • C. Nicolis
  • John S. Nicolis


A chaotic dynamics model creating Markovian strings of symbols as well as sequences of “words” is presented, and its possible relevance to Zipf's law is discussed.

Key words

Chaotic dynamics Markov chains information processing linguistics Zipf's law 


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  1. 1.
    H. G. Schuster,Deterministic Chaos (Physik Verlag, Weinheim, 1984).Google Scholar
  2. 2.
    J. S. Nicolis,Dynamics of Hierarchical systems (Springer, Berlin, 1986).Google Scholar
  3. 3.
    G. K. Zipf,Human Behavior and the Principle of Least Effort (Addison-Wesley, Cambridge, Massachusetts, 1949).Google Scholar
  4. 4.
    E. Montroll and M. F. Shlesinger,J. Stat. Phys. 32:209 (1983).Google Scholar
  5. 5.
    B. West, inLecture Notes in Biomathematics, No. 62 (Springer, Berlin, 1985).Google Scholar
  6. 6.
    B. Mandelbrot,Fractals: Form, Chance, Dimension (Freeman, San Francisco, 1977).Google Scholar
  7. 7.
    G. Nicolis and C. Nicolis,Phys. Rev. 38A:427 (1988).Google Scholar
  8. 8.
    G. Nicolis, S. Rao, G. Rao, and C. Nicolis, inCoherence and Chaos in Dynamical Systems (Manchester University Press, 1988).Google Scholar
  9. 9.
    W. Feller,An Introduction to Probability Theory and Its Applications, 3rd ed. (Wiley, New York, 1968), Vol. I, p. 426.Google Scholar
  10. 10.
    P. Collet and J. P. Eckmann,Iterative maps of the interval as dynamical systems (Birkhäuser, Basel, 1980).Google Scholar
  11. 11.
    P. Gaspard and G. Nicolis,J. Stat. Phys. 31:499 (1983).Google Scholar
  12. 12.
    J. S. Nicolis and I. Tsuda,Progr. Theor. Phys., submitted (1988).Google Scholar

Copyright information

© Plenum Publishing Corporation 1989

Authors and Affiliations

  • G. Nicolis
    • 1
  • C. Nicolis
    • 2
  • John S. Nicolis
    • 3
  1. 1.Faculté des Sciences de l'Université Libre de BruxellesBruxellesBelgium
  2. 2.Institut d'Aéronomie Spatiale de BelgiqueBruxellesBelgium
  3. 3.Department of Electrical EngineeringUniversity of PatrasPatrasGreece

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