What can one learn about Self-Organized Criticality from Dynamical Systems theory ?

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We develop a dynamical system approach for the Zhang's 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 Hausdorff dimensions, and the system size are related to the probability distribution of the avalanche size, via the Ledrappier-Young formula.
23 pages, 8 figures. to appear in Jour. of Stat. Phys

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Statistical Mechanics, Chaotic Dynamics, Mathematical Physics

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http://salesiana.dossiersoluciones.com/handle/123456789/99502

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/cond-mat/9912081
 http://arxiv.org/abs/cond-mat/9912081
 Jour. of Stat. Phys., 98, 375-404 (2000)

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arXiv