Spectrum of multidimensional dynamical systems with positive entropy

Kamiński, B.; Liardet, P.

Studia Mathematica, Tome 108 (1994), p. 77-85 / Harvested from The Polish Digital Mathematics Library

Résumé

Applying methods of harmonic analysis we give a simple proof of the multidimensional version of the Rokhlin-Sinaǐ theorem which states that a Kolmogorov $ℤ^{d}$ -action on a Lebesgue space has a countable Lebesgue spectrum. At the same time we extend this theorem to $ℤ^{\infty}$ -actions. Next, using its relative version, we extend to $ℤ^{\infty}$ -actions some other general results connecting spectrum and entropy.

Publié le : 1994-01-01

Zbl 0824.28011

EUDML-ID : urn:eudml:doc:216042

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     author = {B. Kami\'nski and P. Liardet},
     title = {Spectrum of multidimensional dynamical systems with positive entropy},
     journal = {Studia Mathematica},
     volume = {108},
     year = {1994},
     pages = {77-85},
     zbl = {0824.28011},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv108i1p77bwm}
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Kamiński, B.; Liardet, P. Spectrum of multidimensional dynamical systems with positive entropy. Studia Mathematica, Tome 108 (1994) pp. 77-85. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv108i1p77bwm/

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