An alternative approach to the ergodic theory of measured foliations on surfaces
Author:
- 1 December 1981
- journal article
- research article
- Published by Cambridge University Press (CUP) in Ergodic Theory and Dynamical Systems
- Vol. 1 (4) , 461-488
Abstract
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.Keywords
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