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.
@article{bwmeta1.element.bwnjournal-article-smv110i2p191bwm,
author = {A. Iwanik and Y. Lacroix},
title = {Some constructions of strictly ergodic non-regular Toeplitz flows},
journal = {Studia Mathematica},
volume = {108},
year = {1994},
pages = {191-203},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv110i2p191bwm}
}
Iwanik, A.; Lacroix, Y. Some constructions of strictly ergodic non-regular Toeplitz flows. Studia Mathematica, Tome 108 (1994) pp. 191-203. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv110i2p191bwm/
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