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]).

Comments[edit]

The so-called Rokhlin–Halmos lemma for periodic automorphisms is important for the approximation of an automorphism of a Lebesgue space by periodic transformations (cf. Approximation by periodic transformations), see [a1], p. 75, or [a2], p. 390.

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