Aperiodic automorphism

of a measure space

An automorphism $T$ of a measure space such that its periodic points, i.e. the points $x$ for which $T^k(x) = x$ for some $k>0$, form a set of measure zero. The introduction of a special name for such transformations is due to the fact that in certain theorems of ergodic theory automorphisms with "too many" periodic points are considered as trivial exceptions (see [1]).

References

 [1] V.A. Rokhlin, "Selected topics from the metric theory of dynamical systems" Amer. Math. Soc. Transl. Series 2 , 49 pp. 171–240 Uspekhi Mat. Nauk , 4 : 2 (30) (1949) pp. 57–128