Ergodic theory in concerned with the behavior of dynamic systems on the long run, and provides statistical statements thereof. It delivers a statistical forecast for system, which are otherwise unpredictlable (e.g., chaotic or genuinely stochastic).
This course discusses the mathematical characterization of this situation. A central role is going to be played by the so-called transfer operator, which describes the action of the dynamics on a distribution of states. We are also going to highlight its importance in applications, when it comes to the numerical and data-driven approximation of quantities of interest.