Etienne Matheron : Some remarks regarding ergodic operators

• published: 06 Nov 2015
• views: 4

Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, bibliographies, Mathematics Subject Classification - Multi-criteria search by author, title, tags, mathematical area Let us say that a continuous linear operator T acting on some Polish topological vector space is ergodic if it admits an ergodic probability measure with full support. This talk will be centred in the following question: how can we see that an operator is or is not ergodic? More precisely, I will try (if I'm able to manage my time) to talk about two "positive" results and one "negative" result. The first positive result says that if the operator T acts on a reflexive Banach space and satisfies a strong form of frequent hypercyclicity, then T is ergodic. The second positive result is the well-known criterion for ergodicity relying on the perfect spanning property for unimodular eigenvectors, of which I will outline a "soft" Baire category proof. The negative result will be stated in terms of a parameter measuring the maximal frequency with which (generically) the orbit of a hypercyclic vector for T can visit a ball centred at 0. The talk is based on joint work with Sophie Grivaux. Recording during the thematic meeting: "Frontiers of operator dynamics" the October 1, 2015 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent