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.
@article{bwmeta1.element.bwnjournal-article-smv100i1p13bwm,
author = {Mieczys\l aw Mentzen},
title = {Automorphisms with finite exact uniform rank},
journal = {Studia Mathematica},
volume = {100},
year = {1991},
pages = {13-24},
zbl = {0742.28007},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv100i1p13bwm}
}
Mentzen, Mieczysław. Automorphisms with finite exact uniform rank. Studia Mathematica, Tome 100 (1991) pp. 13-24. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv100i1p13bwm/
[00000] [1] F. M. Dekking, Combinatorial and statistical properties of sequences generated by substitutions, thesis, 1980.
[00001] [2] F. M. Dekking, The spectrum of dynamical systems arising from substitutions of constant length, Z. Wahrsch. Verw. Gebiete 41 (1978), 221-239. | Zbl 0348.54034
[00002] [3] A. del Junco, A transformation with simple spectrum which is not rank one, Canad. J. Math. 29 (3) (1977), 655-633. | Zbl 0335.28010
[00003] [4] A. del Junco, Transformations with discrete spectra are stacking transformations, ibid. 28 (1976), 836-839. | Zbl 0312.47003
[00004] [5] J. King, For mixing transformations rank , Israel J. Math. 56 (1986), 102-122. | Zbl 0626.47012
[00005] [6] M. Lemańczyk and M. K. Mentzen, on metric properties of substitutions, Compositio Math. 65 (1988), 241-263. | Zbl 0696.28009
[00006] [7] D. Newton, On canonical factors of ergodic dynamical systems, J. London Math. Soc. (2) 19 (1979), 129-136. | Zbl 0425.28012
[00007] [8] D. Ornstein, D. Rudolph and B. Weiss, Equivalence of measure preserving transformations, Mem. Amer. Math. Soc. 37 (262) (1982). | Zbl 0504.28019
[00008] [9] M. Queffélec, Substitution Dynamical Systems-Spectral Analysis, Lecture Notes in Math. 1294, Springer, 1987.
[00009] [10] V. A. Rokhlin, On fundamental ideas in measure theory, Mat. Sb. 25 (67) (1) (1949), 107-150 (in Russian)