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

top
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

top

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

top
  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

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.