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Topologically mixing and minimal but not ergodic, analytic transformation onT 5

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Abstract

We give an example of an analytic transformation onT 5 that conserves the Haar measure, that is minimal and topologically mixing, but is not ergodic.

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References

  1. B. R. Fayad. Analytic mixing reparametrizations of irrational flows on the torusT n,n≥3.To appear in Ergodic Theory Dynamical Systems.

  2. H. Furstenberg. Strict ergodicity and transformation of the torus.Amer. J. Math.,83: (1961), 573–601.

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  3. Anatole Katok and Boris Hasselblatt.Introduction to the modern theory of dynamical systems, chapter 4. Cambridge University Press, Cambridge, 1995.

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  4. J-C. Yoccoz.Petits diviseurs en dimension 1. Astérisque (1982), Appendix 1.

  5. Zygmund.Trigonometric series, chapter VI, 6. Cambridge University Press, (1959).

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Authors and Affiliations

  1. Centre de Mathématiques UMR 7640 du CNRS, École Polytechnique, 91128, Palaiseau Cedex, France

    Bassam R. Fayad

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  1. Bassam R. Fayad
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Fayad, B.R. Topologically mixing and minimal but not ergodic, analytic transformation onT 5 . Bol. Soc. Bras. Mat 31, 277–285 (2000). https://doi.org/10.1007/BF01241630

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  • DOI: https://doi.org/10.1007/BF01241630

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