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An alternative approach to the ergodic theory of measured foliations on surfaces

Published online by Cambridge University Press:  19 September 2008

Mary Rees
Mary Rees
Affiliation:
School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA
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Abstract

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We consider measured foliations on surfaces, and interval exchanges. We give alternative proofs of the following theorems first proved by Masur and (independently) Veech. The action of the diffeomorphism group of the surface on the projective space of measured foliations (with respect to a natural ‘Lebesgue’ measure) is ergodic. Almost all measured foliations are uniquely ergodic. Almost all interval exchanges (again, with respect to a natural ‘Lebesgue’ measure) are uniquely ergodic.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 1 , Issue 4 , December 1981 , pp. 461 - 488
Copyright
Copyright © Cambridge University Press 1981

References

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