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Rank two interval exchange transformations*

  • Michael D. Boshernitzan (a1)

Abstract

We consider interval exchange transformations T for which the lengths of the exchanged intervals have linear rank 2 over the field of rationals. We prove that, for such T, minimality implies unique ergodicity. We also provide an algorithm which tests T for aperiodicity and minimality.

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References

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[1]Boshernitzan, M.. A condition for minimal interval exchange maps to be uniquely ergodic. Duke Math. J. 52 (1985), 723752.
[2]Boshernitzan, M.. A unique ergodicity of minimal symbolic flows with linear block growth. J. d'Analyse Math. 44 (1985), 7796.
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[11]Veech, W. A.. Strict ergodicity in zero dimensional dynamical systems and the Kronecker-Weyl theorem mod 2. Trans. Amer. Math. Soc. 140 (1969), 133.
[12]Veech, W. A.. Finite group extensions of irrational rotations. Israel J. Math. 21 (1975), m 240259.
[13]Veech, W. A.. Interval exchange transformations, J. D'Analyse Math. 33 (1978), 222272.
[14]Veech, W. A.. Gauss measures for transformations on the space of interval exchange maps. Ann. of Math. 15 (1982), 201242.
[15]Veech, W. A.. Boshernitzan's criterion for unique ergodicity of an interval exchange transformation. Ergod. Th. & Dynam. Sys. (1987), 7, 149153.
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Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
  • URL: /core/journals/ergodic-theory-and-dynamical-systems
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