Toeplitz -extensions
Annales de l'I.H.P. Probabilités et statistiques (1988)
- Volume: 24, Issue: 1, page 1-43
- ISSN: 0246-0203
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topLemańczyk, Mariusz. "Toeplitz $Z_2$-extensions." Annales de l'I.H.P. Probabilités et statistiques 24.1 (1988): 1-43. <http://eudml.org/doc/77317>.
@article{Lemańczyk1988,
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 = {http://eudml.org/doc/77317},
volume = {24},
year = {1988},
}
TY - JOUR
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 - http://eudml.org/doc/77317
ER -
References
top- [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] P. Collet and J.P. Eckmann, Iterated Maps on the Interval as Dynamical Systems, Birkhäuser, Boston-Basel-Stuttgart, (1980). Zbl0458.58002MR613981
- [3] H. Helson and W. Parry, Cocycles and Spectra, Arkiv för Mat., Vol. 16, 1978, pp. 195-206. Zbl0401.28018MR524748
- [4] K. Jacobs, Ergodic Theory and Combinatorics, Contemp. Math., Vol. 26, 1984, pp. 171- 187. Zbl0548.28006MR737399
- [5] K. Jacobs and M. Keane, 0-1 Sequences of Toeplitz Type, Z. Wahr. verw. Geb., 1969, pp. 123-131. Zbl0195.52703MR255766
- [6] T. Kamae, Spectral Properties of Automaton-Generating Sequences, preprint (unpublished).
- [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] M. Keane, Generalized Morse Sequences, Z. Wahr. verw. Geb., Vol. 10, 1968, pp. 335- 353. Zbl0162.07201MR239047
- [9] J. Kwiatkowski, Isomorphism of Regular Morse Dynamical Systems, Studia Math., Vol. 62, 1982, pp. 59-89. Zbl0525.28018MR665892
- [10] M. Lemańczyk, The Rank of Regular Morse Dynamical Systems, Z. Wahr. verw. Geb., Vol. 70, 1985, pp. 33-48. Zbl0549.28026MR795787
- [11] M. Lemańczyk, Ergodic Properties of Morse Sequences, Thesis, Toruń;, 1985.
- [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] M. Lemańczyk, M.K. Mentzen, On Metric Properties of Substitutions, Compositio Math. (to appear). Zbl0696.28009MR932072
- [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] D. Newton, On Canonical Factors of Ergodic Dynamical Systems, J. Lon. Math. Soc., Vol. 19, 1978, pp. 129-136. Zbl0425.28012MR527744
- [16] M. Queffelec, Contribution à l'étude spectrale de suites arithmétiques, Thèse, 1984 (in French).
- [17] W. Parry, Compact Abelian Group Extensions of Discrete Dynamical Systems, Z. Wahr. verw. Geb., Vol. 13, 1969, pp. 95-113. Zbl0184.26901MR260976
- [18] S. Williams, Toeplitz Minimal Flows Which Are Not Uniquely Ergodic, Z. Wahr. verw. Geb., Vol. 67, 1984, pp. 95-107. Zbl0584.28007MR756807
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- Jakub Kwiatkowski, Mariusz Lemańczyk, On the multiplicity function of ergodic group extensions, II
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- T. Downarowicz, Y. Lacroix, Almost 1-1 extensions of Furstenberg-Weiss type and applications to Toeplitz flows
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