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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:
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 Recent Advances in Topological Dynamics, Lecture Notes in Math. 318, Springer, 1972, pp. 266-276. Zbl 0257.28011, MR 0393424


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