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A condition for unique ergodicity of minimal symbolic flows

Published online by Cambridge University Press:  19 September 2008

Michael D. Boshernitzan
Michael D. Boshernitzan
Affiliation:
Department of Mathematics, Rice University, Houston, Texas 77251, USA
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Abstract

A sufficient condition for unique ergodicity of symbolic flows is provided. In an important but special case of interval exchange transformations, the condition has already been validated by W. Veech.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 12 , Issue 3 , September 1992 , pp. 425 - 428
Copyright
Copyright © Cambridge University Press 1992

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References

REFERENCES

[B1]Boshemitzan, M.. A unique ergodicity of minimal symbolic flows with linear block growth. j d'Analyse Math. 44 (1985), 77–96.CrossRefGoogle Scholar
[B2]Boshemitzan, M.. A condition for minimal interval exchange maps to be uniquely ergodic. Duke Math. J. 52 (3) (1985), 723–752.Google Scholar
[B3]Boshemitzan, M.. Rank two interval exchange maps. Ergod. Th. & Dynam. Sys. 8 (1988), 379–394.CrossRefGoogle Scholar
[Bi]Billingsley, P.. Ergodic Theory and Information. John Wiley & Sons, New York, London, Sydney, 1965.Google Scholar
[Ka]Katok, A.. Invariant measures of flows on oriented surfaces. Dokl. Nauk SSSR 211 (1973),Google Scholar
Sov. Math. Dokl. 14 (1973), 1104–1108.Google Scholar
[Ke]Keane, M.. Non-ergodic interval exchange transformations, Isr. J. Math. 26 (1977), 188–196.CrossRefGoogle Scholar
[V1]Veech, W. A.. Boshernitzan's criterion for unique ergodicity of an interval exchange transformation. Ergod. Th. & Dynam. Sys. 7 (1987), 149–153.CrossRefGoogle Scholar
[V2]Veech, W. A.. Interval exchange transformations. j. d'Analyse Math. 33 (1978), 222–272.CrossRefGoogle Scholar