Frontiers of Operator Theory / Frontières de la théorie des opérateurs

Collection Frontiers of Operator Theory / Frontières de la théorie des opérateurs

Organizer(s) Badea, Catalin ; Bayart, Frédéric ; Gallardo-Gutiérrez, Eva A. ; Grivaux, Sophie ; Lefèvre, Pascal
Date(s) 11/29/21 - 12/3/21
linked URL https://conferences.cirm-math.fr/2388.html
00:00:00 / 00:00:00
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How to shift from frequent hypercyclicity to chaos?

By Quentin Menet

In linear dynamics, chaos requires the density of some orbits and the density of periodic points while frequent hypercyclicity assumes the existence of orbits visiting frequently each non-empty open set. These two notions that we thought were linked are not in general. However, neither are they completely foreign to each other and in particular when we consider the most studied operators in linear dynamics: weighted shifts.

Information about the video

Citation data

  • DOI 10.24350/CIRM.V.19855503
  • Cite this video Menet Quentin (11/30/21). How to shift from frequent hypercyclicity to chaos?. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19855503
  • URL https://dx.doi.org/10.24350/CIRM.V.19855503

Bibliography

  • CHARPENTIER, Stéphane, GROSSE-ERDMANN, Karl, et MENET, Quentin. Chaos and frequent hypercyclicity for weighted shifts. Ergodic Theory and Dynamical Systems, 2021, vol. 41, no 12, p. 3634-3670. - https://doi.org/10.1017/etds.2020.122

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