Advertisement

Journal of Statistical Physics

, Volume 88, Issue 1–2, pp 307–318 | Cite as

A dynamical system approach to SOC models of Zhang's type

  • Ph. Blanchard
  • B. Cessac
  • T. Krüger
Articles

Abstract

We discuss Zhang's model of SOC in the framework of hyperbolic dynamical systems with singularities. The fractal structure of the invariant energy distribution, correlation decay-like phenomena, and symbolic coding are discussed.

Key words

Self-organized criticality hyperbolic dynamical systems with singularities invariant sets and invariant measures fractal structure of the invariant energy distribution 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    P. Bak, C. Tang, K. Wiesenfeld,Phys. Rev. Lett. 59:4, (1987), 381–384, P. Bak, C. Tang, K. Wiesenfeld,Phys. Rev. A. 38:1, (1988), 364–374.MathSciNetCrossRefGoogle Scholar
  2. 2.
    P. Bak, K. Chen,Scientific American, 1991.Google Scholar
  3. 3.
    Ph. Blanchard Ph., B. Cessac, T. Krüger, to be published.Google Scholar
  4. 4.
    A. Katok, J. M. Strelcyn,Lectures notes in Mathematics 1222, (Springer, Berlin, 1986).Google Scholar
  5. 5.
    H. Y. Zhang,Phys. Rev. Let. 63:5 (1988), 470–473; L. Pietronero, P. Tartaglia, Y. C. Zhang,Physica A 173, (1991), 22–44.Google Scholar

Copyright information

© Plenum Publishing Corporation 1997

Authors and Affiliations

  • Ph. Blanchard
    • 1
  • B. Cessac
    • 1
  • T. Krüger
    • 1
  1. 1.Theoretical Physics and BiBoSUniversity of BielefeldBielefeldGermany

Personalised recommendations