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.
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 
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/
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     author = {Kowalski, Zbigniew S.},
     title = {Minimal generators for aperiodic endomorphisms},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {721--725},
     year = {1995},
     volume = {36},
     number = {4},
     mrnumber = {1378693},
     zbl = {0840.28006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_1995_36_4_a9/}
}
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