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Split skew products, a related functional equation, and specification

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Abstract

We prove that a skew product of a measure-preserving transformation with an ergodic automorphism of a compact abelian group is always isomorphic to their direct product via an isomorphism that merely translates the group fibers. This requires solving a functional equation. A weak version of Bowen’s specification property is essential to our construction of a solution.

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Authors and Affiliations

  1. University of Washington, 98195, Seattle, Washington, USA

    D. A. Lind

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  1. D. A. Lind
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Lind, D.A. Split skew products, a related functional equation, and specification. Israel J. Math. 30, 236–254 (1978). https://doi.org/10.1007/BF02761073

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  • DOI: https://doi.org/10.1007/BF02761073

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