Automorphisms with finite exact uniform rank

Mieczysław Mentzen

Studia Mathematica (1991)

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

Abstract

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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.

How to cite

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Mentzen, 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

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  1. [1] F. M. Dekking, Combinatorial and statistical properties of sequences generated by substitutions, thesis, 1980. 
  2. [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. [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. [4] A. del Junco, Transformations with discrete spectra are stacking transformations, ibid. 28 (1976), 836-839. Zbl0312.47003
  5. [5] J. King, For mixing transformations rank ( T k ) = k · r a n k ( T ) , Israel J. Math. 56 (1986), 102-122. Zbl0626.47012
  6. [6] M. Lemańczyk and M. K. Mentzen, on metric properties of substitutions, Compositio Math. 65 (1988), 241-263. Zbl0696.28009
  7. [7] D. Newton, On canonical factors of ergodic dynamical systems, J. London Math. Soc. (2) 19 (1979), 129-136. Zbl0425.28012
  8. [8] D. Ornstein, D. Rudolph and B. Weiss, Equivalence of measure preserving transformations, Mem. Amer. Math. Soc. 37 (262) (1982). Zbl0504.28019
  9. [9] M. Queffélec, Substitution Dynamical Systems-Spectral Analysis, Lecture Notes in Math. 1294, Springer, 1987. 
  10. [10] V. A. Rokhlin, On fundamental ideas in measure theory, Mat. Sb. 25 (67) (1) (1949), 107-150 (in Russian) 

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