Piece-wise affine maps, entropy and dynamical models of self-organized criticality.

Piece-wise affine maps is a nice approximation to nonlinear dynamical systems. Seemingly simple they can possess non-trivial complexity. In this talk I discuss entropy as a fine measure of complexity. I will report some new formulas and inequalities for topological and measure entropy. As an application I consider Zhang model of self-organized criticality, a popular phenomenon to explain an array of physical phenomena. Collapsing of the entropy in thermodynamic limit is closely related to subexponential decay of correlations (criticality) of avalanche observables.

The lecture is mostly based on a collaboration with M.Rypdal.