Ergodic properties of group extensions of dynamical systems with discrete spectra

Mieczysław Mentzen

Studia Mathematica (1991)

  • Volume: 101, Issue: 1, page 19-31
  • ISSN: 0039-3223

Abstract

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Ergodic group extensions of a dynamical system with discrete spectrum are considered. The elements of the centralizer of such a system are described. The main result says that each invariant sub-σ-algebra is determined by a compact subgroup in the centralizer of a normal natural factor.

How to cite

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Mentzen, Mieczysław. "Ergodic properties of group extensions of dynamical systems with discrete spectra." Studia Mathematica 101.1 (1991): 19-31. <http://eudml.org/doc/215890>.

@article{Mentzen1991,
abstract = {Ergodic group extensions of a dynamical system with discrete spectrum are considered. The elements of the centralizer of such a system are described. The main result says that each invariant sub-σ-algebra is determined by a compact subgroup in the centralizer of a normal natural factor.},
author = {Mentzen, Mieczysław},
journal = {Studia Mathematica},
keywords = {ergodic group extensions; dynamical system; discrete spectrum; centralizer},
language = {eng},
number = {1},
pages = {19-31},
title = {Ergodic properties of group extensions of dynamical systems with discrete spectra},
url = {http://eudml.org/doc/215890},
volume = {101},
year = {1991},
}

TY - JOUR
AU - Mentzen, Mieczysław
TI - Ergodic properties of group extensions of dynamical systems with discrete spectra
JO - Studia Mathematica
PY - 1991
VL - 101
IS - 1
SP - 19
EP - 31
AB - Ergodic group extensions of a dynamical system with discrete spectrum are considered. The elements of the centralizer of such a system are described. The main result says that each invariant sub-σ-algebra is determined by a compact subgroup in the centralizer of a normal natural factor.
LA - eng
KW - ergodic group extensions; dynamical system; discrete spectrum; centralizer
UR - http://eudml.org/doc/215890
ER -

References

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  1. [1] A. del Junco and D. Rudolph, On ergodic actions whose self-joinings are graphs, Ergodic Theory Dynamical Systems 7 (1987), 531-557. Zbl0646.60010
  2. [2] H. B. Keynes and D. Newton, Ergodic measures for non-abelian compact group extensions, Compositio Math. 32 (1976), 53-70. Zbl0318.28006
  3. [3] K. Kuratowski and C. Ryll-Nardzewski, A general theorem on selectors, Bull. Acad. Polon. Sci. 13 (1965), 397-403. Zbl0152.21403
  4. [4] M. Lemańczyk and M. K. Mentzen, Compact subgroups in the centralizer of natural factors determine all factors, Ergodic Theory Dynamical Systems 10 (1990), 763-776. Zbl0725.54030
  5. [5] D. Newton, On canonical factors of ergodic dynamical systems, J. London Math. Soc. (2) 19 (1979), 129-136. Zbl0425.28012
  6. [6] D. Rudolph, An example of a measure preserving map with minimal self-joinings, and applications, J. Analyse Math. 35 (1979), 97-122. Zbl0446.28018

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