R.G. Goodwin mentioned that "economists will be led, as natural scientists have been led, to seek in nonlinearities an explanation of the maintenance of oscillation" (Goodwin, Econometrica 19(1), 1951); following this reasoning, we studied business cycles as if they were generated by nonlinear...

In this chapter, we first precise the concept of dynamical systems, and then we introduce the concept of chaos, which is characterized by a sensitive dependence on initial conditions. To quantify this, dynamical (Lyapunov exponents) and probabilistic (dimensions) measures are introduced.