This is the second part of a two-part survey of the modern theory of
nonlinear dynamical systems. We focus on the study of statistical
properties of orbits generated by maps, a field of research known as
ergodic theory. After introducing some basic concepts of measure
theory, we discuss the notions of invariant and ergodic measures and
provide examples of economic applications. The question of
attractiveness and observability, already considered in Part I, is
revisited and the concept of natural, or physical, measure is
explained. This theoretical apparatus then is applied to the question
of predictability of dynamical systems, and the notion of metric
entropy is discussed. Finally, we consider the class of Bernoulli
dynamical systems and discuss the possibility of distinguishing
orbits of deterministic chaotic systems and realizations of
stochastic processes.