Geodesic
Minimal generators for aperiodic endomorphisms
Commentationes Mathematicae Universitatis Carolinae, Tome 36 (1995) no. 4, pp. 721-725.

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Every aperiodic endomorphism $f$ of a nonatomic Lebesgue space which possesses a finite 1-sided generator has a 1-sided generator $\beta $ such that $k_f\leq \operatorname{card}\, \beta \leq k_f+1$. 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.
Classification : 28D05
Keywords: aperiodic endomorphism; 1-sided generator 
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     title = {Minimal generators for aperiodic endomorphisms},
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Kowalski, Zbigniew S. Minimal generators for aperiodic endomorphisms. Commentationes Mathematicae Universitatis Carolinae, Tome 36 (1995) no. 4, pp. 721-725. http://geodesic.mathdoc.fr/item/CMUC_1995__36_4_a9/