Chargé de recherche CNRS
CEREMADE, Université Paris Dauphine & IMCCE, Observatoire de Paris

Lecture notes for the Master course "Hamiltonians Systems and Perturbation Theory" (this is just a preliminary version)

Papers (these are just the preliminary versions, you can write to me if you want the final versions)

29. Hamiltonian perturbation theory for ultra-differentiable functions, with J. Féjoz, 101p, Memoirs of the AMS, to appear 
28. KAM, α-Gevrey regularity and the α-Bruno-Rüssmann condition, with J. Féjoz, 53p, Annali Scuola Norm. Sup. Pisa, to appear 
26. Double exponential stability of quasi-periodic motion in Hamiltonian systems, with B. Fayad and L.Niederman, Communication in Mathematical Physics, 350, no. 1, 361-386 (2017) 
25. Some instability properties of resonant invariant tori in Hamiltonian systemsMathematical Research Letters, 24, no. 1, 21-35 (2017)
24. Generic perturbations of linear integrable Hamiltonian systemsRegular and Chaotic Dynamics, 21, no. 6, 665-681 (2016)
23. Nekhoroshev’s estimates for quasi-periodic time-dependent perturbationsCommentarii Mathematici Helvetici, 91, no. 4, 653-703 (2016)
22. Non-degenerate Liouville tori are KAM stableAdvances in Mathematics, 292, 42-51 (2016)
21. Ergodization time for linear flows on tori via geometry of numbers, Archiv der Mathematik, 106, no. 2, 129-133 (2016)
20. A note on micro-instability for Hamiltonian systems close to integrable, with V. Kaloshin, Proceedings of the AMS, 144, no. 4, 1553-1560 (2016)
19. A KAM theorem through Dirichlet's box and Khintchine's transference principlesMoscow Mathematical Journal, 14, no. 4, 1-13 (2014)
18. The classical KAM theorem for Hamiltonian systems via rational approximations, with S. Fischler, Regular and Chaotic Dynamics, 19, no. 2, 251-265 (2014).
17. Generic fast diffusion for a class of non-convex Hamiltonians with two degrees of freedom, with V. KaloshinMoscow Mathematical Journal, 14, no. 2, 181-203 (2014) 
14. Normal forms, stability and splitting of invariant manifolds I. Gevrey Hamiltonians, Regular and Chaotic Dynamics, 18, no. 3, 237-260 (2013).
13. A geometrical proof of the persistence of normally hyperbolic submanifolds, with P. Berger, Dynamical Systems: An International Journal, 28, no. 4, 567-581 (2013).
12. A Diophantine duality applied to the KAM and Nekhoroshev theorems, with S. Fischler, Mathematische Zeitschrift, 275, no. 3, 1135-1167 (2013).
11. A more applicable notion of effective stability for Hamiltonian systems, CRAS Mecanique, 340, no. 6, 401-404 (2012).
10. Optimal stability and instability for near-linear Hamiltonians, Annales Henri Poincaré, 13, no. 4, 857-868 (2012). [AHP Distinguished Paper 2012].
9. An example of instability in high-dimensional Hamiltonian systems, International Mathematics Research Notices, 2012, no. 3, 685-716 (2012).
8. Instability for a priori unstable Hamiltonian systems: a dynamical approach, with E. Pennamen, DCDS - Series A, 32, no. 3, 753-793 (2012).
7. Generic Nekhoroshev theory without small divisors, with L. Niederman, Annales de l'Institut Fourier, 62, no. 1, 277-324 (2012). 
6. Transition between stability and instability for Hamiltonian systems close to integrable, Oberwolfach Reports, Dynamische System, 8, 3 (2011). [Non-peer reviewed, 3p.]
5. Effective stability for Gevrey and finitely differentiable prevalent Hamiltonians, Communication in Mathematical Physics, 307, no. 1, 157-183 (2011).
4. Generic super-exponential stability of invariant tori in Hamiltonian systems, Ergodic Theory and Dynamical Systems, 31, no.5, 1287-1303 (2011).
3. Improved exponential stability for near-integrable Hamiltonian systems, with J.-P. Marco, Nonlinearity, 24, no. 1, 97-112 (2011).
2. Nekhoroshev estimates for finitely differentiable quasi-convex Hamiltonians, Journal of Differential Equations, 249, no. 11, 2905-2920 (2010).
0. Stabilité et instabilité des systèmes hamiltoniens presque-intégrables, PhD thesis, Université Paris Sud, Orsay (2010). [PhD thesis, advisors: L. Niederman and J.-P. Marco]
1. Simplicité des groupes de transformations de surfaces, Ensaios Matematicos, SBM, 14, 1-143 (2008). [Master thesis, advisor: F. Le Roux]