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A short proof of ergodicity of Babillot-Ledrappier measures


Author: Rita Solomyak
Journal: Proc. Amer. Math. Soc. 129 (2001), 3589-3591
MSC (2000): Primary 37A20
Published electronically: May 10, 2001
MathSciNet review: 1860491
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Abstract:

Let $ M $ be a compact manifold, and let ${\phi_t}$ be a transitive homologically full Anosov flow on $M$. Let $ \widetilde{M} $ be a $\mathbb{Z}^d$-cover for $ M $, and let $\widetilde{\phi_t} $ be the lift of ${\phi_t}$ to $\widetilde{M}$. Babillot and Ledrappier exhibited a family of measures on $\widetilde{M}$, which are invariant and ergodic with respect to the strong stable foliation of $\widetilde{\phi_t}$. We provide a new short proof of ergodicity.


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Additional Information

Rita Solomyak
Affiliation: Department of Mathematics, University of Washington, Box 35450, Seattle, Washington 98195
Email: rsolom@math.washington.edu

DOI: https://doi.org/10.1090/S0002-9939-01-06181-0
Received by editor(s): April 14, 2000
Published electronically: May 10, 2001
Communicated by: Michael Handel
Article copyright: © Copyright 2001 American Mathematical Society