  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.
