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Journal of Statistical Physics

, Volume 98, Issue 1–2, pp 375–404 | Cite as

What Can One Learn About Self-Organized Criticality from Dynamical Systems Theory?

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

Abstract

We develop a dynamical system approach for the Zhang model of self-organized criticality, for which the dynamics can be described either in terms of iterated function systems or as a piecewise hyperbolic dynamical system of skew-product type. In this setting we describe the SOC attractor, and discuss its fractal structure. We show how the Lyapunov exponents, the Haussdorf dimensions, and the system size are related to the probability distribution of the avalanche size via the Ledrappier–Young formula.

self-organized criticality hyperbolic dynamical systems iterated functions systems 

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Copyright information

© Plenum Publishing Corporation 2000

Authors and Affiliations

  • Ph. Blanchard
    • 1
  • B. Cessac
    • 2
  • T. Krüger
    • 1
    • 3
  1. 1.University of Bielefeld, BiBoSBielefeldGermany
  2. 2.Institut Non Linéaire de NiceValbonneFrance
  3. 3.Technische UniversitaetBerlinGermany

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