# Article

 Title: Minimal generators for aperiodic endomorphisms (English) Author: Kowalski, Zbigniew S. Language: English Journal: Commentationes Mathematicae Universitatis Carolinae ISSN: 0010-2628 (print) ISSN: 1213-7243 (online) Volume: 36 Issue: 4 Year: 1995 Pages: 721-725 . Category: math . 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 $k_f\leq \operatorname{card}\, \beta \leq k_f+1$. 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. (English) Keyword: aperiodic endomorphism Keyword: 1-sided generator MSC: 28D05 idZBL: Zbl 0840.28006 idMR: MR1378693 . Date available: 2009-01-08T18:21:15Z Last updated: 2012-04-30 Stable URL: http://hdl.handle.net/10338.dmlcz/118799 . Reference: [1] Denker M., Grillenberger Ch., Sigmund K.: Ergodic Theory on Compact Spaces.Lecture Notes in Math. 527, Springer, 1976. Zbl 0328.28008, MR 0457675 Reference: [2] Kowalski Z.S.: Minimal generators for ergodic endomorphisms.Studia Mathematica 16 (1988), 85-88. Zbl 0676.28009, MR 0985076 Reference: [3] Parry W.: Entropy and Generators in Ergodic Theory.Benjamin, 1969. Zbl 0175.34001, MR 0262464 Reference: [4] Rohlin V.A.: On the fundamental ideas of measure theory.Amer. Math. Soc. Transl. Ser. 1 10 (1962), 1-54 Mat. Sb. 25 (1949), 107-150. MR 0030584 Reference: [5] Walters P.: Some results on the classification of non-invertible measure preserving transformations.in: Recent Advances in Topological Dynamics, Lecture Notes in Math. 318, Springer, 1972, pp. 266-276. Zbl 0257.28011, MR 0393424 .

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