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Prime flows in topological dynamics

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Abstract

We present some results in topological dynamics and number theory. The number-theoretical results are estimates of the rates of convergence of sequences {fx26-1}, wherena is irrational,a is taken mod 1, and 0<β<1. One of these results is used to construct a homorphismT of a compact metric spaceX such that the minimal flow (X, T) had no nontrivial homomorphic images, i.e. is a prime flow. We define an infinite family of such flows, and describe other interesting properties of these flows.

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Authors and Affiliations

  1. Institute of Mathematics, The Hebrew University, Jerusalem, Israel

    Harry Furstenberg, Harvey Keynes & Leonard Shapiro

  2. University of Minnesota, Minneapolis, Minnesota, U.S.A.

    Harry Furstenberg, Harvey Keynes & Leonard Shapiro

Authors
  1. Harry Furstenberg
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  2. Harvey Keynes
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  3. Leonard Shapiro
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Additional information

The research of all of the authors was supported by NSF Grant 28071.

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Furstenberg, H., Keynes, H. & Shapiro, L. Prime flows in topological dynamics. Israel J. Math. 14, 26–38 (1973). https://doi.org/10.1007/BF02761532

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  • DOI: https://doi.org/10.1007/BF02761532

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