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A non-regular Toeplitz flow with preset pure point spectrum

T. Downarowicz; Y. Lacroix

Studia Mathematica (1996)

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

Abstract

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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.

How to cite

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Downarowicz, 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

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  1. [B-K1] W. Bułatek and J. Kwiatkowski, The topological centralizers of Toeplitz flows and their ℤ 2 -extensions, Publ. Math. 34 (1990), 45-65. Zbl0731.54027
  2. [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
  3. [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
  4. [D] T. Downarowicz, The Choquet simplex of invariant measures for minimal flows, Israel J. Math. 74 (1991), 241-256. Zbl0746.58047
  5. [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
  6. [G-H] W. Gottschalk and G. A. Hedlund, Topological Dynamics, Amer. Math. Soc. Colloq. Publ. 36, 1955. 
  7. [F] H. Furstenberg, Strict ergodicity and transformations of the torus, Amer. J. Math. 83 (1961), 573-601. Zbl0178.38404
  8. [I] A. Iwanik, Toeplitz flows with pure point spectrum, preprint. Zbl0888.28008
  9. [I-L] A. Iwanik and Y. Lacroix, Some constructions of strictly ergodic non-regular Toeplitz flows, Studia Math. 110 (1994), 191-203. Zbl0810.28009
  10. [J-K] K. Jacobs and M. Keane, 0-1 sequences of Toeplitz type, Z. Wahrsch. Verw. Gebiete 13 (1969), 123-131. Zbl0195.52703
  11. [O] J. C. Oxtoby, Ergodic sets, Bull. Amer. Math. Soc. 58 (1952), 116-136. Zbl0046.11504
  12. [W] S. Williams, Toeplitz minimal flows which are not uniquely ergodic, Z. Wahrsch. Verw. Gebiete 67,(1984), 95-107. Zbl0584.28007

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