For more information about this meeting, contact Federico Rodriguez Hertz, Stephanie Zerby, Anatole Katok, Boris Kalinin, Dmitri Burago.

Title: | Ergodic properties of skew products in infinite measure |

Seminar: | Center for Dynamics and Geometry Seminars |

Speaker: | Yuri Lima, Weizmann Institute of Science, Israel |

Abstract: |

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 |

Date: | 03 / 11 / 2013 |

Time: | 03:35pm - 04:35pm |