Measures of dependence: application to one-dimensional dynamical systems
Résumé
Even a simple and deterministic dynamical system may behave "impredictably". One says that the system presents a "chaotic" behavior. Choosing two initial conditions close to each other, one may observe, after a finite time, two orbits which are totally diferent. This motivates the study of the statistical properties of dynamical systems. We will introduce in this talk several measures of dependence which will allow to derive interesting stochastic properties for two classes of one-dimensional expanding dynamical systems.