Approximations of Dynamical Systems

The constructive theory of functions studies the relationship between the properties of functions and the speed of their approximations by functions of some particular fixed class. In a similar way, in ergodic theory we may study the dependence of various properties of dynamical systems on the rapidity of their approximations by the periodic dynamical systems which are simplest from some point of view. We shall see that many properties of dynamical systems are intimately related to the character of their approximations.