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AC 1 expanding map of the circle which is not weak-mixing

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Abstract

In this paper, we construct an example of aC 1 expanding map of the circle which preserves Lebesgue measure such that the system is ergodic, but not weak-mixing. This contrasts with the case ofC 1+ε maps, where any such map preserving Lebesgue measure has a Bernoulli natural extension and hence is weak-mixing.

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Authors and Affiliations

  1. Statistical Laboratory, Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, 16 Mill Lane, CB2 1SB, Cambridge, England

    Anthony N. Quas

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  1. Anthony N. Quas
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Correspondence to Anthony N. Quas.

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Quas, A.N. AC 1 expanding map of the circle which is not weak-mixing. Israel J. Math. 93, 359–372 (1996). https://doi.org/10.1007/BF02761112

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  • DOI: https://doi.org/10.1007/BF02761112

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