Toeplitz Z 2 -extensions

Mariusz Lemańczyk

Annales de l'I.H.P. Probabilités et statistiques (1988)

  • Volume: 24, Issue: 1, page 1-43
  • ISSN: 0246-0203

How to cite


Lemańczyk, Mariusz. "Toeplitz $Z_2$-extensions." Annales de l'I.H.P. Probabilités et statistiques 24.1 (1988): 1-43. <>.

author = {Lemańczyk, Mariusz},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {ergodic automorphisms; -extensions; spectral multiplicity; generalized Morse sequences; Lebesgue spectral component},
language = {eng},
number = {1},
pages = {1-43},
publisher = {Gauthier-Villars},
title = {Toeplitz $Z_2$-extensions},
url = {},
volume = {24},
year = {1988},

AU - Lemańczyk, Mariusz
TI - Toeplitz $Z_2$-extensions
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 1988
PB - Gauthier-Villars
VL - 24
IS - 1
SP - 1
EP - 43
LA - eng
KW - ergodic automorphisms; -extensions; spectral multiplicity; generalized Morse sequences; Lebesgue spectral component
UR -
ER -


  1. [1] G. Christol, T. Kamae, M. Mendès-France and G. Rauzy, Suites algébriques, automates et substitutions, Bull. Soc. Math. France, T. 108, 1980, pp. 401-419 (in French). Zbl0472.10035MR614317
  2. [2] P. Collet and J.P. Eckmann, Iterated Maps on the Interval as Dynamical Systems, Birkhäuser, Boston-Basel-Stuttgart, (1980). Zbl0458.58002MR613981
  3. [3] H. Helson and W. Parry, Cocycles and Spectra, Arkiv för Mat., Vol. 16, 1978, pp. 195-206. Zbl0401.28018MR524748
  4. [4] K. Jacobs, Ergodic Theory and Combinatorics, Contemp. Math., Vol. 26, 1984, pp. 171- 187. Zbl0548.28006MR737399
  5. [5] K. Jacobs and M. Keane, 0-1 Sequences of Toeplitz Type, Z. Wahr. verw. Geb., 1969, pp. 123-131. Zbl0195.52703MR255766
  6. [6] T. Kamae, Spectral Properties of Automaton-Generating Sequences, preprint (unpublished). 
  7. [7] A.B. Katok and A.M. Stepin, Approximation in Ergodic Theory, Usp. Mat. Nauk, Vol. 22, (137), 1967, pp. 81-105 (in Russian). Zbl0172.07202MR219697
  8. [8] M. Keane, Generalized Morse Sequences, Z. Wahr. verw. Geb., Vol. 10, 1968, pp. 335- 353. Zbl0162.07201MR239047
  9. [9] J. Kwiatkowski, Isomorphism of Regular Morse Dynamical Systems, Studia Math., Vol. 62, 1982, pp. 59-89. Zbl0525.28018MR665892
  10. [10] M. Lemańczyk, The Rank of Regular Morse Dynamical Systems, Z. Wahr. verw. Geb., Vol. 70, 1985, pp. 33-48. Zbl0549.28026MR795787
  11. [11] M. Lemańczyk, Ergodic Properties of Morse Sequences, Thesis, Toruń;, 1985. 
  12. [12] M. Lemańczyk, Ergodic Z2-Extensions Over Rational Pure Point Spectrum, Category and Homomorphisms, Compositio Math., Vol. 63, 1987, pp. 63-81. Zbl0629.28013MR906379
  13. [13] M. Lemańczyk, M.K. Mentzen, On Metric Properties of Substitutions, Compositio Math. (to appear). Zbl0696.28009MR932072
  14. [14] J. Mathew and M.G. Nadkarni, A Measure-Preserving Transformation Whose Spectrum has Lebesgue Component of Multiplicity Two, Bull. Lon. Math. Soc., Vol. 16, 1984, pp. 402-406. Zbl0515.28010MR749448
  15. [15] D. Newton, On Canonical Factors of Ergodic Dynamical Systems, J. Lon. Math. Soc., Vol. 19, 1978, pp. 129-136. Zbl0425.28012MR527744
  16. [16] M. Queffelec, Contribution à l'étude spectrale de suites arithmétiques, Thèse, 1984 (in French). 
  17. [17] W. Parry, Compact Abelian Group Extensions of Discrete Dynamical Systems, Z. Wahr. verw. Geb., Vol. 13, 1969, pp. 95-113. Zbl0184.26901MR260976
  18. [18] S. Williams, Toeplitz Minimal Flows Which Are Not Uniquely Ergodic, Z. Wahr. verw. Geb., Vol. 67, 1984, pp. 95-107. Zbl0584.28007MR756807

Citations in EuDML Documents

  1. I. Filipowicz, Product d -actions on a Lebesgue space and their applications
  2. Krzysztof Frączek, Cyclic space isomorphism of unitary operators
  3. Jean-Paul Allouche, Pierre Liardet, Generalized Rudin-Shapiro sequences
  4. G. Goodson, J. Kwiatkowski, M. Lemańczyk, P. Liardet, On the multiplicity function of ergodic group extensions of rotations
  5. Jakub Kwiatkowski, Mariusz Lemańczyk, On the multiplicity function of ergodic group extensions, II
  6. Sébastien Ferenczi, Jan Kwiatkowski, Rank and spectral multiplicity
  7. T. Downarowicz, Y. Lacroix, Almost 1-1 extensions of Furstenberg-Weiss type and applications to Toeplitz flows
  8. Jan Kwiatkowski, Yves Lacroix, Finite rank transformation and weak closure theorem
  9. Sébastien Ferenczi, Systems of finite rank

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