Minimal generators for aperiodic endomorphisms

Zbigniew S. Kowalski

Commentationes Mathematicae Universitatis Carolinae (1995)

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

Abstract

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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 β such that k f ≤ card β ≤ 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.

How to cite

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Kowalski, 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

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

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