For more information about this meeting, contact Federico Rodriguez Hertz, Robin Enderle, Anatole Katok, Dmitri Burago.
| Title: | Ergodic properties of skew products in infinite measure |
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| Seminar: | Center for Dynamics and Geometry Seminar |
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| Speaker: | Yuri Lima, Weizmann Institute of Science, Israel |
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| Abstract: |
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| Let (Ω,μ) be a shift of finite type with a Markov probability, and (Y,ν) a non-atomic standard measure space. For each symbol i of the symbolic space, let Φ_i be a measure-preserving automorphism of (Y,ν). We study skew products of the form (ω; y) -> (σω,Φ_ω_0 (y)), where σ is the shift map on (Ω,μ). We prove that, when the skew product is conservative, it is ergodic if and only if the Φ_i's have no common non-trivial invariant set.
In the second part we study the skew product when Ω={0,1}^Z, μ is a Bernoulli measure, and Φ_0, Φ_1 are IR-extensions of a same uniquely ergodic probability-preserving automorphism. We prove that, for a large class of roof functions, the skew product is rationally ergodic with return sequence asymptotic to √n, and its trajectories satisfy the central, functional central and local limit theorem.
Joint work with Patricia Cirilo and Enrique Pujals. |
Room Reservation Information
| Room Number: | MB114 |
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| Date: | 03 / 11 / 2013 |
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| Time: | 03:35pm - 04:35pm |
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