Toeplitz flows with pure point spectrum

A. Iwanik

Studia Mathematica (1996)

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

Abstract

top
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.

How to cite

top

Iwanik, 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
  1. [B-K] W. Bułatek and J. Kwiatkowski, Strictly ergodic Toeplitz flows with positive entropies and trivial centralizers, Studia Math. 103 (1992), 133-142. Zbl0816.58028
  2. [D] T. Downarowicz, The Choquet simplex of invariant measures for minimal flows, Israel J. Math. 74 (1991), 241-256. Zbl0746.58047
  3. [D-I] T. Downarowicz and A. Iwanik, Quasi-uniform convergence in compact dynamical systems, Studia Math. 89 (1988), 11-25. Zbl0665.54029
  4. [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
  5. [G] C. Grillenberger, Zwei kombinatorische Konstruktionen für strikt ergodische Folgen, thesis, Univ. Erlangen-Nürnberg, 1970. 
  6. [H] G. A. Hedlund, Sturmian minimal sets, Amer. J. Math. 66 (1944), 605-620. Zbl0063.01982
  7. [I-L] A. Iwanik and Y. Lacroix, Some constructions of strictly ergodic non-regular Toeplitz flows, Studia Math. 110 (1994), 191-203. Zbl0810.28009
  8. [J-K] K. Jacobs and M. Keane, 0-1 sequences of Toeplitz type, Z. Wahrsch. Verw. Gebiete 13 (1969), 123-131. Zbl0195.52703
  9. [W] S. Williams, Toeplitz minimal flows which are not uniquely ergodic, ibid. 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.