Toeplitz flows with pure point spectrum

A. Iwanik

Studia Mathematica (1996)

  • Volume: 118, Issue: 1, page 27-35
  • ISSN: 0039-3223

Abstract

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We construct strictly ergodic 0-1 Toeplitz flows with pure point spectrum and irrational eigenvalues. It is also shown that the property of being regular is not a measure-theoretic invariant for strictly ergodic Toeplitz flows.

How to cite

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Iwanik, A.. "Toeplitz flows with pure point spectrum." Studia Mathematica 118.1 (1996): 27-35. <http://eudml.org/doc/216261>.

@article{Iwanik1996,
abstract = {We construct strictly ergodic 0-1 Toeplitz flows with pure point spectrum and irrational eigenvalues. It is also shown that the property of being regular is not a measure-theoretic invariant for strictly ergodic Toeplitz flows.},
author = {Iwanik, A.},
journal = {Studia Mathematica},
keywords = {Toeplitz sequence; Sturmian sequence; group extension; pure point spectrum; strict ergodicity},
language = {eng},
number = {1},
pages = {27-35},
title = {Toeplitz flows with pure point spectrum},
url = {http://eudml.org/doc/216261},
volume = {118},
year = {1996},
}

TY - JOUR
AU - Iwanik, A.
TI - Toeplitz flows with pure point spectrum
JO - Studia Mathematica
PY - 1996
VL - 118
IS - 1
SP - 27
EP - 35
AB - We construct strictly ergodic 0-1 Toeplitz flows with pure point spectrum and irrational eigenvalues. It is also shown that the property of being regular is not a measure-theoretic invariant for strictly ergodic Toeplitz flows.
LA - eng
KW - Toeplitz sequence; Sturmian sequence; group extension; pure point spectrum; strict ergodicity
UR - http://eudml.org/doc/216261
ER -

References

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  1. [B-K] W. Bułatek and J. Kwiatkowski, Strictly ergodic Toeplitz flows with positive entropies and trivial centralizers, Studia Math. 103 (1992), 133-142. 
  2. [D] T. Downarowicz, The Choquet simplex of invariant measures for minimal flows, Israel J. Math. 74 (1991), 241-256. 
  3. [D-I] T. Downarowicz and A. Iwanik, Quasi-uniform convergence in compact dynamical systems, Studia Math. 89 (1988), 11-25. 
  4. [D-K-L] T. Downarowicz, J. Kwiatkowski and Y. Lacroix, A criterion for Toeplitz flows to be topologically isomorphic and applications, Colloq. Math. 68 (1995), 219-228. 
  5. [G] C. Grillenberger, Zwei kombinatorische Konstruktionen für strikt ergodische Folgen, thesis, Univ. Erlangen-Nürnberg, 1970. 
  6. [H] G. A. Hedlund, Sturmian minimal sets, Amer. J. Math. 66 (1944), 605-620. 
  7. [I-L] A. Iwanik and Y. Lacroix, Some constructions of strictly ergodic non-regular Toeplitz flows, Studia Math. 110 (1994), 191-203. 
  8. [J-K] K. Jacobs and M. Keane, 0-1 sequences of Toeplitz type, Z. Wahrsch. Verw. Gebiete 13 (1969), 123-131. 
  9. [W] S. Williams, Toeplitz minimal flows which are not uniquely ergodic, ibid. 67 (1984), 95-107. 

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