Minimal generators for aperiodic endomorphisms. (English) Zbl 0840.28006

Kowalski, Zbigniew S.

Commentat. Math. Univ. Carol. 36, No. 4, 721-725 (1995).

Summary: Every aperiodic endomorphism \(f\) of a nonatomic Lebesgue space which possesses a finite 1-sided generator has a 1-sided generator \(\beta\) such that \(k_f\leq \text{card } \beta\leq k_f+ 1\). This is the best estimate for the minimal cardinality of a 1-sided generator. The above result is the generalization of the analogous one for ergodic case.

MSC:

28D05

Measure-preserving transformations

Keywords:

aperiodic endomorphism; one-sided generator