| 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 |
| . |
