A non-regular Toeplitz flow with preset pure point spectrum
Downarowicz, T. ; Lacroix, Y.
Studia Mathematica, Tome 119 (1996), p. 235-246 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

Given an arbitrary countable subgroup σ0 of the torus, containing infinitely many rationals, we construct a strictly ergodic 0-1 Toeplitz flow with pure point spectrum equal to σ0. 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.

Publié le : 1996-01-01
EUDML-ID : urn:eudml:doc:216334 
@article{bwmeta1.element.bwnjournal-article-smv120i3p235bwm,
     author = {T. Downarowicz and Y. Lacroix},
     title = {A non-regular Toeplitz flow with preset pure point spectrum},
     journal = {Studia Mathematica},
     volume = {119},
     year = {1996},
     pages = {235-246},
     zbl = {0888.28009},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv120i3p235bwm}
}

Downarowicz, T.; Lacroix, Y. A non-regular Toeplitz flow with preset pure point spectrum. Studia Mathematica, Tome 119 (1996) pp. 235-246. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv120i3p235bwm/

[00000] [B-K1] W. Bułatek and J. Kwiatkowski, The topological centralizers of Toeplitz flows and their ℤ2-extensions, Publ. Math. 34 (1990), 45-65. | Zbl 0731.54027

[00001] [B-K2] W. Bułatek and J. Kwiatkowski, Strictly ergodic Toeplitz flows with positive entropies and trivial centralizers, Studia Math. 103 (1992), 133-142. | Zbl 0816.58028

[00002] [D-G-S] M. Denker, C. Grillenberger and K. Sigmund, Ergodic Theory on Compact Spaces, Lecture Notes in Math. 527, Springer, Berlin, 1976. | Zbl 0328.28008

[00003] [D] T. Downarowicz, The Choquet simplex of invariant measures for minimal flows, Israel J. Math. 74 (1991), 241-256. | Zbl 0746.58047

[00004] [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. | Zbl 0820.28009

[00005] [G-H] W. Gottschalk and G. A. Hedlund, Topological Dynamics, Amer. Math. Soc. Colloq. Publ. 36, 1955.

[00006] [F] H. Furstenberg, Strict ergodicity and transformations of the torus, Amer. J. Math. 83 (1961), 573-601. | Zbl 0178.38404

[00007] [I] A. Iwanik, Toeplitz flows with pure point spectrum, preprint. | Zbl 0888.28008

[00008] [I-L] A. Iwanik and Y. Lacroix, Some constructions of strictly ergodic non-regular Toeplitz flows, Studia Math. 110 (1994), 191-203. | Zbl 0810.28009

[00009] [J-K] K. Jacobs and M. Keane, 0-1 sequences of Toeplitz type, Z. Wahrsch. Verw. Gebiete 13 (1969), 123-131. | Zbl 0195.52703

[00010] [O] J. C. Oxtoby, Ergodic sets, Bull. Amer. Math. Soc. 58 (1952), 116-136. | Zbl 0046.11504

[00011] [W] S. Williams, Toeplitz minimal flows which are not uniquely ergodic, Z. Wahrsch. Verw. Gebiete 67,(1984), 95-107. | Zbl 0584.28007