In several recent papers a new
approach has been developed in the theory of approximation of automorphisms.
Using this approach, Katok and Stepin have developed a new method which is very
powerful and which has enabled them to solve several problems which had remained
open for some time. Among the results they obtained is a characterization of
automorphisms which are not strongly mixing in terms of the speed with which they
can be approximated. Counter-examples may be given to show that the
speed of approximation cannot be used to characterize those automorphisms
which have continuous spectrum. In this paper certain related concepts are
developed which do make it possible to deal in general with automorphisms
which have continuous spectrum, and to distinguish those which are not
strongly mixing from those which are strongly mixing among them. Since it is
well-known that automorphisms have continuous spectrum if and only if they are
weakly mixing, the result serves to distinguish between strong and weak
mixing.
