A class of generalized Ornstein transformations with the weak mixing property

El Houcein El Abdalaoui

Annales de l'I.H.P. Probabilités et statistiques (2000)

  • Volume: 36, Issue: 6, page 775-786
  • ISSN: 0246-0203

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El Abdalaoui, El Houcein. "A class of generalized Ornstein transformations with the weak mixing property." Annales de l'I.H.P. Probabilités et statistiques 36.6 (2000): 775-786. <http://eudml.org/doc/77679>.

@article{ElAbdalaoui2000,
author = {El Abdalaoui, El Houcein},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {weak-mixing; cutting and stacking; Ornstein transformations; interval exchanges},
language = {eng},
number = {6},
pages = {775-786},
publisher = {Gauthier-Villars},
title = {A class of generalized Ornstein transformations with the weak mixing property},
url = {http://eudml.org/doc/77679},
volume = {36},
year = {2000},
}

TY - JOUR
AU - El Abdalaoui, El Houcein
TI - A class of generalized Ornstein transformations with the weak mixing property
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2000
PB - Gauthier-Villars
VL - 36
IS - 6
SP - 775
EP - 786
LA - eng
KW - weak-mixing; cutting and stacking; Ornstein transformations; interval exchanges
UR - http://eudml.org/doc/77679
ER -

References

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  1. [1] Bourgain J., On the spectral type of Ornstein's class one transformations, Israel J. Math.84 (1993) 53-63. Zbl0787.28011MR1244658
  2. [2] Blum J.R., Cogburn R., On ergodic sequences of measures, Proc. Amer. Math. Soc.51 (1975) 359-365. Zbl0309.43001MR372529
  3. [3] Choksi J.R., Nadkarni M.G., The group of eigenvalues of a rank one transformation, Canad. Math. Bull.38 (1) (1995) 42-54. Zbl0833.28008MR1319899
  4. [4] El Abdalaoui E.H., A large class of Ornstein transformations with mixing property, Canad. Math. Bull., to appear. Zbl0967.37005MR1754020
  5. [5] El Abdalaoui E.H., La singularité mutuelle presque sûre du spectre des transformations d'Ornstein, Israel J. Math.112 (1999) 135-156. Zbl0967.37004MR1715002
  6. [6] Friedman N.A., Introduction to Ergodic Theory, Van Nostrand - Reinhold, New York, 1970. Zbl0212.40004MR435350
  7. [7] Friedman N.A., Replication and stacking in ergodic theory, Amer. Math. Monthly99 (1992) 31-34. Zbl0760.28012MR1140275
  8. [8] Kuipers L., Niederreiter H., Uniform Distribution of Sequences, Wiley-Interscience, New York, 1974. Zbl0281.10001MR419394
  9. [9] Nadkarni M.G., Spectral Theory of Dynamical Systems, Hindustan Book Agency, New Delhi, 1998; To appear in Europe under Birkhauser. Zbl1038.37502MR1719722
  10. [10] Nogueira A., Rudolph D., Topological weak-mixing of interval exchange maps, Ergodic Theory Dynamical Systems17 (1997) 1183-1209. Zbl0958.37010MR1477038
  11. [11] Ornstein D.S., On the root problem in ergodic theory, in: Proc. Sixth Berkeley Symposium in Math. Statistics and Probability, University of California Press, 1971, pp. 347-356. Zbl0262.28009MR399415
  12. [12] Thouvenot J.-P., private communication. 
  13. [13] Veech W.A., A criterion for a process to be prime, Monatsh. Math.94 (1982) 335-341. Zbl0499.28016MR685378

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