# Some constructions of strictly ergodic non-regular Toeplitz flows

Studia Mathematica (1994)

- Volume: 110, Issue: 2, page 191-203
- ISSN: 0039-3223

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topIwanik, A., and Lacroix, Y.. "Some constructions of strictly ergodic non-regular Toeplitz flows." Studia Mathematica 110.2 (1994): 191-203. <http://eudml.org/doc/216108>.

@article{Iwanik1994,

abstract = {We give a necessary and sufficient condition for a Toeplitz flow to be strictly ergodic. Next we show that the regularity of a Toeplitz flow is not a topological invariant and define the "eventual regularity" as a sequence; its behavior at infinity is topologically invariant. A relation between regularity and topological entropy is given. Finally, we construct strictly ergodic Toeplitz flows with "good" cyclic approximation and non-discrete spectrum.},

author = {Iwanik, A., Lacroix, Y.},

journal = {Studia Mathematica},

keywords = {strict ergodicity; regularity; cyclic approximation; Toeplitz flows; shift dynamical system},

language = {eng},

number = {2},

pages = {191-203},

title = {Some constructions of strictly ergodic non-regular Toeplitz flows},

url = {http://eudml.org/doc/216108},

volume = {110},

year = {1994},

}

TY - JOUR

AU - Iwanik, A.

AU - Lacroix, Y.

TI - Some constructions of strictly ergodic non-regular Toeplitz flows

JO - Studia Mathematica

PY - 1994

VL - 110

IS - 2

SP - 191

EP - 203

AB - We give a necessary and sufficient condition for a Toeplitz flow to be strictly ergodic. Next we show that the regularity of a Toeplitz flow is not a topological invariant and define the "eventual regularity" as a sequence; its behavior at infinity is topologically invariant. A relation between regularity and topological entropy is given. Finally, we construct strictly ergodic Toeplitz flows with "good" cyclic approximation and non-discrete spectrum.

LA - eng

KW - strict ergodicity; regularity; cyclic approximation; Toeplitz flows; shift dynamical system

UR - http://eudml.org/doc/216108

ER -

## References

top- [Co-Fo-Si] I. P. Cornfeld, S. V. Fomin and Ya. G. Sinai, Ergodic Theory, Springer, 1982.
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- [Do-Kw-La] T. Downarowicz, J. Kwiatkowski and Y. Lacroix, A criterion for Toeplitz flows to be isomorphic and applications, preprint. Zbl0820.28009
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- [Ke] M. Keane, Generalized Morse sequences, ibid. 10 (1968), 335-353. Zbl0162.07201
- [La1] Y. Lacroix, Contribution à l'étude des suites de Toeplitz et numération en produit infini, Thesis, Université de Provence, 1992.
- [La2] Y. Lacroix, Metric properties of generalized Cantor products, Acta Arith. 63 (1993), 61-77. Zbl0774.11042
- [Le] M. Lemańczyk, Ergodic ${Z}_{2}$-extensions over rational pure point spectrum, category and homomorphisms, Compositio Math. 63 (1987), 63-81. Zbl0629.28013
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- [Wi] S. Williams, Toeplitz minimal flows which are not uniquely ergodic, Z. Wahrsch. Verw. Gebiete 67 (1984), 95-107. Zbl0584.28007

## Citations in EuDML Documents

top- T. Downarowicz, Y. Lacroix, A non-regular Toeplitz flow with preset pure point spectrum
- T. Downarowicz, Jan Kwiatkowski, Y. Lacroix, Spectral isomorphisms of Morse flows
- A. Iwanik, Toeplitz flows with pure point spectrum
- T. Downarowicz, Y. Lacroix, Almost 1-1 extensions of Furstenberg-Weiss type and applications to Toeplitz flows
- Sébastien Ferenczi, Systems of finite rank

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