# Automorphisms with finite exact uniform rank

Studia Mathematica (1991)

- Volume: 100, Issue: 1, page 13-24
- ISSN: 0039-3223

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topMentzen, Mieczysław. "Automorphisms with finite exact uniform rank." Studia Mathematica 100.1 (1991): 13-24. <http://eudml.org/doc/215869>.

@article{Mentzen1991,

abstract = {The notion of exact uniform rank, EUR, of an automorphism of a probability Lebesgue space is defined. It is shown that each ergodic automorphism with finite EUR is finite extension of some automorphism with rational discrete spectrum. Moreover, for automorphisms with finite EUR, the upper bounds of EUR of their factors and ergodic iterations are computed.},

author = {Mentzen, Mieczysław},

journal = {Studia Mathematica},

keywords = {ergodic automorphism; finite rank; exact uniform rank; stack; rational discrete spectrum},

language = {eng},

number = {1},

pages = {13-24},

title = {Automorphisms with finite exact uniform rank},

url = {http://eudml.org/doc/215869},

volume = {100},

year = {1991},

}

TY - JOUR

AU - Mentzen, Mieczysław

TI - Automorphisms with finite exact uniform rank

JO - Studia Mathematica

PY - 1991

VL - 100

IS - 1

SP - 13

EP - 24

AB - The notion of exact uniform rank, EUR, of an automorphism of a probability Lebesgue space is defined. It is shown that each ergodic automorphism with finite EUR is finite extension of some automorphism with rational discrete spectrum. Moreover, for automorphisms with finite EUR, the upper bounds of EUR of their factors and ergodic iterations are computed.

LA - eng

KW - ergodic automorphism; finite rank; exact uniform rank; stack; rational discrete spectrum

UR - http://eudml.org/doc/215869

ER -

## References

top- [1] F. M. Dekking, Combinatorial and statistical properties of sequences generated by substitutions, thesis, 1980.
- [2] F. M. Dekking, The spectrum of dynamical systems arising from substitutions of constant length, Z. Wahrsch. Verw. Gebiete 41 (1978), 221-239. Zbl0348.54034
- [3] A. del Junco, A transformation with simple spectrum which is not rank one, Canad. J. Math. 29 (3) (1977), 655-633. Zbl0335.28010
- [4] A. del Junco, Transformations with discrete spectra are stacking transformations, ibid. 28 (1976), 836-839. Zbl0312.47003
- [5] J. King, For mixing transformations rank $\left({T}^{k}\right)=k\xb7rank\left(T\right)$, Israel J. Math. 56 (1986), 102-122. Zbl0626.47012
- [6] M. Lemańczyk and M. K. Mentzen, on metric properties of substitutions, Compositio Math. 65 (1988), 241-263. Zbl0696.28009
- [7] D. Newton, On canonical factors of ergodic dynamical systems, J. London Math. Soc. (2) 19 (1979), 129-136. Zbl0425.28012
- [8] D. Ornstein, D. Rudolph and B. Weiss, Equivalence of measure preserving transformations, Mem. Amer. Math. Soc. 37 (262) (1982). Zbl0504.28019
- [9] M. Queffélec, Substitution Dynamical Systems-Spectral Analysis, Lecture Notes in Math. 1294, Springer, 1987.
- [10] V. A. Rokhlin, On fundamental ideas in measure theory, Mat. Sb. 25 (67) (1) (1949), 107-150 (in Russian)

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