This is the second part of a two-part survey of the modern theory ofnonlinear dynamical systems. We focus on the study of statisticalproperties of orbits generated by maps, a field of research known asergodic theory. After introducing some basic concepts of measuretheory, we discuss the notions of invariant and ergodic measures andprovide examples of economic applications. The question ofattractiveness and observability, already considered in Part I, isrevisited and the concept of natural, or physical, measure isexplained. This theoretical apparatus then is applied to the questionof predictability of dynamical systems, and the notion of metricentropy is discussed. Finally, we consider the class of Bernoullidynamical systems and discuss the possibility of distinguishingorbits of deterministic chaotic systems and realizations ofstochastic processes.