# Minimal generators for aperiodic endomorphisms

Commentationes Mathematicae Universitatis Carolinae (1995)

- Volume: 36, Issue: 4, page 721-725
- ISSN: 0010-2628

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topKowalski, Zbigniew S.. "Minimal generators for aperiodic endomorphisms." Commentationes Mathematicae Universitatis Carolinae 36.4 (1995): 721-725. <http://eudml.org/doc/247702>.

@article{Kowalski1995,

abstract = {Every aperiodic endomorphism $f$ of a nonatomic Lebesgue space which possesses a finite 1-sided generator has a 1-sided generator $\beta $ such that $k_f\le \operatorname\{card\}\, \beta \le k_f+1$. 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.},

author = {Kowalski, Zbigniew S.},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {aperiodic endomorphism; 1-sided generator; aperiodic endomorphism; one-sided generator},

language = {eng},

number = {4},

pages = {721-725},

publisher = {Charles University in Prague, Faculty of Mathematics and Physics},

title = {Minimal generators for aperiodic endomorphisms},

url = {http://eudml.org/doc/247702},

volume = {36},

year = {1995},

}

TY - JOUR

AU - Kowalski, Zbigniew S.

TI - Minimal generators for aperiodic endomorphisms

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 1995

PB - Charles University in Prague, Faculty of Mathematics and Physics

VL - 36

IS - 4

SP - 721

EP - 725

AB - Every aperiodic endomorphism $f$ of a nonatomic Lebesgue space which possesses a finite 1-sided generator has a 1-sided generator $\beta $ such that $k_f\le \operatorname{card}\, \beta \le k_f+1$. 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.

LA - eng

KW - aperiodic endomorphism; 1-sided generator; aperiodic endomorphism; one-sided generator

UR - http://eudml.org/doc/247702

ER -

## References

top- Denker M., Grillenberger Ch., Sigmund K., Ergodic Theory on Compact Spaces, Lecture Notes in Math. 527, Springer, 1976. Zbl0328.28008MR0457675
- Kowalski Z.S., Minimal generators for ergodic endomorphisms, Studia Mathematica 16 (1988), 85-88. (1988) Zbl0676.28009MR0985076
- Parry W., Entropy and Generators in Ergodic Theory, Benjamin, 1969. Zbl0175.34001MR0262464
- 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. (1949) MR0030584
- 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. Zbl0257.28011MR0393424

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