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Boshernitzan's criterion for unique ergodicity of an interval exchange transformation

Published online by Cambridge University Press:  19 September 2008

William A. Veech
William A. Veech
Affiliation:
Department of Mathematics, Wiess School of Natural Sciences, Rice University, P.O. Box 1892, Houston, Texas 77251, USA
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Abstract

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Confirming a conjecture by Boshernitzan, it is proved that if T is a minimal non-uniquely ergodic interval exchange, the minimum spacing of the partition determined by Tn is O(1/n).

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 7 , Issue 1 , March 1987, pp. 149 - 153
Copyright
Copyright © Cambridge University Press 1987

References

REFERENCES

[1]Boshernitzan, M., A condition for minimal interval exchange maps to be uniquely ergodic. Duke Math. J. 52 (1985), 723–752.Google Scholar
[2]Boshernitzan, M.. In preparation.Google Scholar
[3]Gutkin, E.. Billiards on almost integrable polyhedral surfaces. Ergod. Th. & Dynatm. Sys., 4 (1984), 569–584.Google Scholar
[5]Veech, W. A.. Finite group extensions of irrational rotations. Israel J. Math. 21 (1975), 240–259.Google Scholar
[4]Veech, W. A.. Strict ergodicity in zero dimensional dynamical systems and the Kronecker-Weyl theorem mod 2. Trans. Amer. Math. Soc., 140 (1969), 1–33.Google Scholar
[6]Veech, W. A.. Letter to E. Gutkin, August 10, 1983.Google Scholar