Models of spatially extended systems

This series of lectures aims to provide an overview on Coupled Map Lattices as models of spatially extended dynamical systems. Some definitions and generalities about this class of models are reported. Moreover, two specific examples are used for describing their generic properties. In particular, attention is focused on the presence of Chaotic Transients in both periodic and chaotic Coupled Map Lattices, suggesting a close link with complex Cellular Automata evolution rules. The methods used for a quantitative analysis of the dynamical properties have been also presented in some detail. The technical difficulties encountered in a mathematically rigorous description of a seemingly trivial class of models have also been proposed for pedagogical reasons.