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ArticleOriginal scientific text

Title

Spectrum of multidimensional dynamical systems with positive entropy

Authors 1, 2

Affiliations

  1. Institute of Mathematics, Nicholas Copernicus University, Chopina 12/18, 87-100 Toruń, Poland
  2. Groupe de Théorie des Nombres, Université de Provence, 3, Place Victor Hugo, F-13331 Marseille Cedex 3, France

Abstract

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

Bibliography

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Studia Mathematica
1994/108/1
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Pages:
77-85
Main language of publication
English
Received
1993-03-03
Published
1994
Exact and natural sciences