# A non-regular Toeplitz flow with preset pure point spectrum

Studia Mathematica (1996)

- Volume: 120, Issue: 3, page 235-246
- ISSN: 0039-3223

## Access Full Article

top## Abstract

top## How to cite

topDownarowicz, T., and Lacroix, Y.. "A non-regular Toeplitz flow with preset pure point spectrum." Studia Mathematica 120.3 (1996): 235-246. <http://eudml.org/doc/216334>.

@article{Downarowicz1996,

abstract = {Given an arbitrary countable subgroup $σ_0$ of the torus, containing infinitely many rationals, we construct a strictly ergodic 0-1 Toeplitz flow with pure point spectrum equal to $σ_0$. For a large class of Toeplitz flows certain eigenvalues are induced by eigenvalues of the flow Y which can be seen along the aperiodic parts.},

author = {Downarowicz, T., Lacroix, Y.},

journal = {Studia Mathematica},

keywords = {Toeplitz sequence; pure point spectrum; strict ergodicity; group extension},

language = {eng},

number = {3},

pages = {235-246},

title = {A non-regular Toeplitz flow with preset pure point spectrum},

url = {http://eudml.org/doc/216334},

volume = {120},

year = {1996},

}

TY - JOUR

AU - Downarowicz, T.

AU - Lacroix, Y.

TI - A non-regular Toeplitz flow with preset pure point spectrum

JO - Studia Mathematica

PY - 1996

VL - 120

IS - 3

SP - 235

EP - 246

AB - Given an arbitrary countable subgroup $σ_0$ of the torus, containing infinitely many rationals, we construct a strictly ergodic 0-1 Toeplitz flow with pure point spectrum equal to $σ_0$. For a large class of Toeplitz flows certain eigenvalues are induced by eigenvalues of the flow Y which can be seen along the aperiodic parts.

LA - eng

KW - Toeplitz sequence; pure point spectrum; strict ergodicity; group extension

UR - http://eudml.org/doc/216334

ER -

## References

top- [B-K1] W. Bułatek and J. Kwiatkowski, The topological centralizers of Toeplitz flows and their ${\mathbb{Z}}_{2}$-extensions, Publ. Math. 34 (1990), 45-65. Zbl0731.54027
- [B-K2] W. Bułatek and J. Kwiatkowski, Strictly ergodic Toeplitz flows with positive entropies and trivial centralizers, Studia Math. 103 (1992), 133-142. Zbl0816.58028
- [D-G-S] M. Denker, C. Grillenberger and K. Sigmund, Ergodic Theory on Compact Spaces, Lecture Notes in Math. 527, Springer, Berlin, 1976. Zbl0328.28008
- [D] T. Downarowicz, The Choquet simplex of invariant measures for minimal flows, Israel J. Math. 74 (1991), 241-256. Zbl0746.58047
- [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. Zbl0820.28009
- [G-H] W. Gottschalk and G. A. Hedlund, Topological Dynamics, Amer. Math. Soc. Colloq. Publ. 36, 1955.
- [F] H. Furstenberg, Strict ergodicity and transformations of the torus, Amer. J. Math. 83 (1961), 573-601. Zbl0178.38404
- [I] A. Iwanik, Toeplitz flows with pure point spectrum, preprint. Zbl0888.28008
- [I-L] A. Iwanik and Y. Lacroix, Some constructions of strictly ergodic non-regular Toeplitz flows, Studia Math. 110 (1994), 191-203. Zbl0810.28009
- [J-K] K. Jacobs and M. Keane, 0-1 sequences of Toeplitz type, Z. Wahrsch. Verw. Gebiete 13 (1969), 123-131. Zbl0195.52703
- [O] J. C. Oxtoby, Ergodic sets, Bull. Amer. Math. Soc. 58 (1952), 116-136. Zbl0046.11504
- [W] S. Williams, Toeplitz minimal flows which are not uniquely ergodic, Z. Wahrsch. Verw. Gebiete 67,(1984), 95-107. Zbl0584.28007