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Topological and metric product\(\mathbb{Z}^d \)-actions and their applications-actions and their applications

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Abstract

We show that for a\(\mathbb{Z}^2 \)-action Ψ being the Kronecker sum of a symbolic strictly ergodic\(\mathbb{Z}\)-actionT and a Chacon\(\mathbb{Z}\)-actionS, the rank (covering number) of Ψ is the same as that forT. Using this result we construct, for a given natural numberr≥2 and a real numberb∈(0,1) withr\b≥1, a\(\mathbb{Z}^d \)-action with rankr, covering numberb and a simple spectrum. On the other hand, for any positive integersr, m with 1≤m≤r≤∞ we construct a\(\mathbb{Z}^d \)-action with rankr and spectral multiplicitym.

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Authors and Affiliations

  1. Library Management and Scientific Information, Pedagogical University of Bydgoszcz (WSP), Grabowa 2, 85-067, Bydgoszcz, Poland

    I. Filipowicz (Chair)

  2. Faculty of Mathematics and Informatics, Nicholas Copernicus University, Chopina 12/18, 87-100, Toruń, Poland

    B. Kamiński & J. Kwiatkowski

Authors
  1. I. Filipowicz
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  2. B. Kamiński
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  3. J. Kwiatkowski
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Correspondence to I. Filipowicz.

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Filipowicz, I., Kamiński, B. & Kwiatkowski, J. Topological and metric product\(\mathbb{Z}^d \)-actions and their applications-actions and their applications. J. Anal. Math. 83, 21–39 (2001). https://doi.org/10.1007/BF02790255

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  • DOI: https://doi.org/10.1007/BF02790255

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