Modul:   MAT760  Ergodic Theory and Dynamical Systems Seminar

e-Seminar: Extensions with shrinking fibers

Talk by Prof. Dr. Benoît Kloeckner

Date: 25.05.20  Time: 13.45 - 14.45  Room: Y27H28

Let T and S be two discrete-time dynamical systems, the first being an extension of the second with a contracting dynamics along the fibers in a very general meaning. The main goal of the talk will be to show the simple result, yet not known in this generality before, that every S-invariant measure has a unique T-invariant lift. Then, many properties of invariant measures can easily be lifted as well (ergodicity, mixing, physicality, entropy) possibly under additional mild assumptions. The main tool is a variant of the Wasserstein distance issued from optimal transportation. If time permits, we shall evoke the lighting of more subtle properties (statistical properties, speed of decay of correlations).