Automorphisms that admit an approximation by periodic transformations

Summary We are concerned with a class of automorphisms which can be approximated by periodic transformations. We show that such an automorphism T is ergodic and that a relationship exists between the spectrum of T, the measure of the sets which are invariant under T, and the ergodicity of the powers of T. Finally, we exhibit conditions under which T is weakly mixing and not strongly mixing.This research was supported by NSF Grant No. GP-7490.