# Toeplitz flows with pure point spectrum

Studia Mathematica (1996)

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

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topIwanik, 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

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

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