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A mixingT for whichT-T −1 is Bernoulli

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Abstract

We show that if σ is the Bernoulli shift on sequences of {−1, 1} with equiprobable product measure andT is a suitable mixing entropy zero trnsformation then the skew product defined byS(x,y)=(σx,T x0 y) is Bernoulli.

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References

  1. Adler, R., Shields, P.: Skew products of Bernoulli shifts with rotations. Isr. J. Math.12, 215–220 (1972).

    Google Scholar 

  2. Adler, R., Shields, P.: Skew products of Bernoulli shifts with rotations. II. Isr. J. Math.19, 228–236 (1974).

    Google Scholar 

  3. Kalikow, S.:T-T −1 transformation is not loose Bernoulli. Ann. Math. (To appear).

  4. Meilijson, I.: Mixing properties of a class of skew products. Isr. J. Math.19, 266–270 (1974).

    Google Scholar 

  5. Ornstein, D. S.: A mixing transformation that commutes only with its powers. Proc. 6th Berkeley Symp. Math. Stat. Prob. II, pp. 335–360. Berkeley-Los Angeles: Univ. California Press. 1967.

    Google Scholar 

  6. Ornstein, D. S.: AK-automorphism with no square root and Pinsker's conjecture. Adv. Math.10, 89–102 (1973).

    Google Scholar 

  7. Shields, P.: Weak and very weak Bernoulli partitions. Mh. Math.84, 133–142 (1977).

    Google Scholar 

  8. Shields, P., Burton, R.: A skew product which is Bernoulli. Mh. Math.86, 155–165 (1978).

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Oregon State University, 97331, Corvallis, OR, USA

    Robert M. Burton

  2. Department of Mathematics, Toledo, Ohio, USA

    Paul C. Shields

Authors
  1. Robert M. Burton
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  2. Paul C. Shields
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Additional information

Research supported in part by NSF Grant MCS-8005172.

Research supported in part by NSG Grants MCS-807739-A02 and MCS-8024091.

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Burton, R.M., Shields, P.C. A mixingT for whichT-T −1 is Bernoulli. Monatshefte für Mathematik 95, 89–98 (1983). https://doi.org/10.1007/BF01323652

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  • DOI: https://doi.org/10.1007/BF01323652

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