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]
4. Menet Quentin. "Inverse of
frequently hypercyclic operators", Journal of the Institute of
Mathematics of Jussieu (2022), 21, 1867-1886. [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]
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]
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]
14. Menet Quentin. "Invariant subspaces for
non-normable Fréchet spaces", Advances in Mathematics (2018), 339,
495-539 [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]