November 2008 December 2008 January 2009 Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa 1 1 2 3 4 5 6 1 2 3 2 3 4 5 6 7 8 7 8 9 10 11 12 13 4 5 6 7 8 9 10 9 10 11 12 13 14 15 14 15 16 17 18 19 20 11 12 13 14 15 16 17 16 17 18 19 20 21 22 21 22 23 24 25 26 27 18 19 20 21 22 23 24 23 24 25 26 27 28 29 28 29 30 31 25 26 27 28 29 30 31 30 |

4:00 pm Tuesday, December 2, 2008 Ergodic Theory Seminar: Unique ergodicity of horocyclic foliations revisitedby Alexey Glutsyuk (ENS Lyon) in HB227- This is a joint work with Mikhail Lyubich. It is well-known (classical results by Bowen et al) that a (minimal) unstable foliation of an Anosov diffeomorphism (or flow) on a compact manifold is always uniquely ergodic. We prove a generalization that works for its analogues in complex dynamics: the quotient horospheric laminations associated to hyperbolic rational functions distinct from powers. The above-mentioned quotient horospheric laminations were introduced by M.Lyubich. They come from the extension (due to M.Lyubich and Y.Minsky) of the Thurston dictionary between Kleinian groups and rational dynamics. Their topology is related to the asymptotic behavior of the derivatives of the iterations of a rational function. Their minimality was previously proved by the speaker. A canonical transversal invariant measure was constructed in a joint work by V.Kaimanovich and M.Lyubich. For these laminations the classical unique ergodicity proofs do not work. Bowen's proof uses Markov partitions. Our proof is purely geometric and does not use Markov partitions.
Submitted by maxine@rice.edu |