A short proof of ergodicity of Babillot-Ledrappier measures
HTML articles powered by AMS MathViewer
- by Rita Solomyak PDF
- Proc. Amer. Math. Soc. 129 (2001), 3589-3591 Request permission
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.References
- J. Aaronson and M. Denker. On exact group extensions. Preprint (1999) .
- Martine Babillot and François Ledrappier, Geodesic paths and horocycle flow on abelian covers, Lie groups and ergodic theory (Mumbai, 1996) Tata Inst. Fund. Res. Stud. Math., vol. 14, Tata Inst. Fund. Res., Bombay, 1998, pp. 1–32. MR 1699356
- Rufus Bowen, Equilibrium states and the ergodic theory of Anosov diffeomorphisms, Lecture Notes in Mathematics, Vol. 470, Springer-Verlag, Berlin-New York, 1975. MR 0442989
- Rufus Bowen and Brian Marcus, Unique ergodicity for horocycle foliations, Israel J. Math. 26 (1977), no. 1, 43–67. MR 451307, DOI 10.1007/BF03007655
- Y. Guivarc’h, Propriétés ergodiques, en mesure infinie, de certains systèmes dynamiques fibrés, Ergodic Theory Dynam. Systems 9 (1989), no. 3, 433–453 (French, with English summary). MR 1016662, DOI 10.1017/S0143385700005083
- Richard Sharp, Closed orbits in homology classes for Anosov flows, Ergodic Theory Dynam. Systems 13 (1993), no. 2, 387–408. MR 1235480, DOI 10.1017/S0143385700007434
Additional Information
- Rita Solomyak
- Affiliation: Department of Mathematics, University of Washington, Box 35450, Seattle, Washington 98195
- Email: rsolom@math.washington.edu
- Received by editor(s): April 14, 2000
- Published electronically: May 10, 2001
- Communicated by: Michael Handel
- © Copyright 2001 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 3589-3591
- MSC (2000): Primary 37A20
- DOI: https://doi.org/10.1090/S0002-9939-01-06181-0
- MathSciNet review: 1860491