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Research area My research area mainly concerns linear
dynamics and invariant subspaces. - Linear dynamics is the theory of studying the
properties of
orbits of linear and continuous operators on Banach spaces or
Fréchet spaces. Persons who are interested in this theory could appreciate the
books Linear Chaos and Dynamics of Linear Operators. - The study of invariant subspaces consists in
determining which operators T do not possess closed subspaces M (different
to {0} and the whole space) so that T(M) is included in M and which spaces
support such operators. Beside this research, I have worked on model
checking and game theory. Publications 1. Preprints 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
published in peer-review 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), 3634-3670 [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
published in conference proceedings 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. Popular
mathematics 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]
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]
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", Advances in
Mathematics (2018), 339, 495-539 [arxiv/journal]