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Domaine de recherches Mes recherches concernent principalement la
dynamique linéaire et l’étude des sous-espaces invariants - La dynamique linéaire est le domaine de
l'analyse fonctionnelle qui étudie le comportement des orbites d'opérateurs
linéaires et continus sur un espace de Banach ou un espace de Fréchet. Les
personnes intéressées par ce domaine peuvent apprécier les livres Linear Chaos et Dynamics of Linear Operators. - L’étude des sous-espaces invariants
consiste à déterminer quels opérateurs T ne possèdent pas de sous-espaces
fermés M tels que T(M) est inclus dans M (autre que {0} et l’espace
complet) et quels espaces supportent de tels opérateurs. A côté de ces recherches, j’ai également
mené des travaux en théorie de la vérification et en théorie des jeux. Publications 1. Articles soumis 1.
Grivaux Sophie, Mathéron Etienne, Menet Quentin. "Generic
properties of lp-contractions and similar
operator topologies", [arxiv] 2.
López-Martínez Antoni, Menet Quentin. "Two remarks on the set of recurrent vectors",
[arxiv] 2. Articles publiés dans des journaux avec comité de lecture 1.
Menet Quentin, Papathanasiou Dimitris.
"Structure of sets of bounded sequences with a prescribed number of
accumulation points", Proceedings of the American Mathematical Society
[arxiv] 2.
Bayart Frédéric, Costa Jr. Fernando, Menet Quentin. "Common
hypercyclic vectors and dimension of the parameter set", Indiana
University Mathematics Journal (2022), 71, 1763-1795 [arxiv/journal] 3.
Martin
Özgür, Menet Quentin, Puig Yunied.
"Disjoint
frequently hypercyclic pseudo-shifts", Journal of Functional Analysis
(2022), 283, 44p [arxiv/journal] 5.
Grivaux Sophie, Matheron
Etienne, Menet Quentin. "Does a typical lp-space
contraction have a non-trivial invariant subspace?", Transactions of
the American Mathematical Society (2021), 374, 7359-7410 [arxiv/journal] 6.
Charpentier
Stéphane, Grosse-Erdmann Karl, Menet Quentin. "Chaos and
frequent hypercyclicity for weighted shifts", Ergodic Theory and
Dynamical Systems (2021), 41, 3634-3670 [arxiv/journal] 7.
Grivaux Sophie, Matheron
Etienne, Menet Quentin. “Linear dynamical systems
on Hilbert spaces: Typical properties and explicit examples”, Memoirs
of the American Mathematical Society (2021), 269,
1315, 1-147 [arxiv/journal] 13. Menet
Quentin. "Existence of common hypercyclic subspaces for the derivative
operator and the translation operators", Revista
de la Real Academia de Ciencias Exactas, Físicas y Naturales (2019), 113, 487-505 [arxiv/journal] 15.
Menet Quentin. "Linear chaos and
frequent hypercyclicity", Transactions of the American Mathematical
Society (2017), 369, 4977-4994 [arxiv/journal] 16. Bès Juan, Menet Quentin, Peris Alfredo, Puig Yunied. "Recurrence
properties of hypercyclic operators", Mathematische
Annalen (2016), 366, 545-572 [arxiv/journal] 17. Bayart Frédéric, Ernst Romuald, Menet Quentin. "Non-existence
of frequently hypercyclic subspaces for P(D)", Israel Journal of
Mathematics (2016), 214, 149-166 [journal] 18. Charpentier
Stéphane, Ernst Romuald, Menet Quentin. "Gamma-supercyclicity",
Journal of Functional Analysis (2016), 270, 4443-4465 [arxiv/journal] 19. Bès Juan, Menet Quentin. "Existence of
common and upper frequently hypercyclic subspaces", Journal of
Mathematical Analysis and Applications (2015), 432, 10-37 [arxiv/journal] 20. Brihaye Thomas, Haddad Axel, Menet Quentin.
"Simple strategies for Banach-Mazur games and sets of probability
1", Information and Computation (2015), 245, 17–35 [journal] 21. Menet
Quentin. "Existence and non-existence of frequently hypercyclic
subspaces for weighted shifts", Proceedings of the American
Mathematical Society (2015), 143, 2469-2477 [arxiv/journal] 22. Menet
Quentin. "Hereditarily hypercyclic subspaces", Journal of
Operator Theory (2015), 73, 385-405 [arxiv/journal] 23. Bertrand
Nathalie, Bouyer Patricia, Brihaye Thomas, Menet
Quentin, Baier Christel, Groesser Marcus, Jurdzinski
Marcin. "Stochastic Timed Automata" Logical Methods in Computer
Science (2014) 10, 1-73 [arxiv/journal] 24. Charpentier Stéphane, Menet Quentin, Mouze
Augustin. "Closed universal subspaces of spaces of infinitely
differentiable functions" Annales de l'Institut
Fourier (2014), 64, 297-325 [journal] 25. Menet
Quentin. "Hypercyclic subspaces and weighted shifts" Advances in
Mathematics (2014), 255, 305-337 [arxiv/journal] 26.
Menet Quentin. "Hypercyclic Subspaces on Fréchet Spaces Without
Continuous Norm", Integral Equations and Operator Theory (2013), 77,
489-520 [arxiv/journal] 27. Menet Quentin. "Sous-espaces fermés
de séries universelles sur un espace de Fréchet" Studia Mathematica
(2011), 207, 181-195 [journal] 3. Articles publiés dans des actes de conference 1.
Bouyer Patricia, Brihaye
Thomas, Carlier Pierre, Menet Quentin, "Compositional Design of
Stochastic Timed Automata", CSR 2016, Computer Science: Theory and
Applications Volume 9691 of the series Lecture Notes in Computer Science,
117-130 [journal] 2. Brihaye Thomas, Menet Quentin. "Simple
strategies for Banach-Mazur games and fairly correct systems" in
International Symposium on Games, Automata, Logics and Formal Verification
2013, EPTCS 119, 21-34 [arxiv/journal] 3. Bouyer
Patricia, Brihaye Thomas, Jurdzinski
Marcin, Menet Quentin. "Almost-Sure Model-Checking of Reactive Timed
Automata.", QEST 2012, IEEE Computer Society Press, 138-147 [pdf]
4. Articles
de vulgarisation 1. Grosse-Erdmann
Karl, Menet Quentin. "Le chaos linéaire: un paradoxe? ", Interstices, 2012 [journal] 2. Brihaye Thomas et Menet Quentin. "Topology, probability, games and verification",
Notes de la cinquième BSSM, 2013 [journal]
4. Menet Quentin. "Inverse of
frequently hypercyclic operators", Journal of the Institute of
Mathematics of Jussieu (2022), 21, 1867-1886. [arxiv/journal]
8. Menet
Quentin. "Invariant subspaces for Fréchet spaces without
continuous norm", Proceedings of the
American Mathematical Society (2021), 149, 8, 3379-3393 [arxiv/journal]
9. Ernst Romuald, Esser Céline, Menet
Quentin. "U-frequent hypercyclicity notions and related
weighted densities", Israel Journal of Mathematics (2021), 241, 817-848 [arxiv/journal]
10. Menet Quentin. "Inverse of U-frequently
hypercyclic operators", Journal of Functional Analysis (2020), 279 [arxiv/journal]
11. Menet
Quentin. "A bridge between U-frequent hypercyclicity and
frequent hypercyclicity",
Journal of Mathematical Analysis and Applications (2020), 482 [arxiv/journal]
12. Bès Juan, Menet Quentin, Peris Alfredo, Puig Yunied. "Strong transitivity properties for
operators", Journal of Differential Equations (2019), 266, 1313-1337 [arxiv/journal]
14. Menet Quentin. "Invariant
subspaces for non-normable Fréchet spaces"
(2018), Advances in Mathematics, 339, 495-539 [arxiv/journal]