m
• E

F Nous contacter

0

Multi angle

H 1 Some remarks regarding ergodic operators

Auteurs : Matheron, Etienne (Auteur de la Conférence)
CIRM (Editeur )

Résumé : 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.

Codes MSC :
37A05 - Measure-preserving transformations
47A16 - Cyclic vectors, hypercyclic and chaotic operators
47A35 - Ergodic theory of linear operators

 Informations sur la Vidéo Langue : Anglais Date de publication : 03/11/15 Date de captation : 01/10/15 Sous collection : Research talks Format : MP4 arXiv category : Dynamical Systems ; Functional Analysis Domaine : Dynamical Systems & ODE Durée : 00:53:30 Audience : Chercheurs ; Doctorants , Post - Doctorants Download : https://videos.cirm-math.fr/2015-10-01_Matheron.mp4 Informations sur la rencontre Nom de la rencontre : Frontiers of operator dynamics / Frontières de la dynamique linéaireOrganisateurs de la rencontre : Grivaux, Sophie ; Lemanczyk, Marius ; Tomilov, YuriDates : 28/09/15 - 02/10/15 Année de la rencontre : 2015 URL Congrès : http://conferences.cirm-math.fr/1125.htmlCitation Data DOI : 10.24350/CIRM.V.18844203 Cite this video as: Matheron, Etienne (2015). Some remarks regarding ergodic operators. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18844203 URI : http://dx.doi.org/10.24350/CIRM.V.18844203

Bibliographie

1. Grivaux, S., & Matheron, E. (2014). Invariant measures for frequently hypercyclic operators. Advances in Mathematics, 265, 371-427 - http://dx.doi.org/10.1016/j.aim.2014.08.002

Titres de périodiques et e-books électroniques (Depuis le CIRM)

Ressources Electroniques

Books & Print journals

Recherche avancée

0
Z