We report the results of a joint analysis of data from BICEP2/Keck Array and Planck. BICEP2 and Keck Array have observed the same approximately 400â€‰â€‰deg^{2} patch of sky centered on RA 0 h, Dec.â€¦ (More)

In this paper, we prove a version of Arnolâ€™d-Liouville theorem for C commuting Hamiltonians. We show that the Lipschitz regularity of the foliation by invariant Lagrangian tori is crucial toâ€¦ (More)

Let M be a closed and connected manifold, H : T âˆ—MÃ—R/Zâ†’R a Tonelli 1-periodic Hamiltonian and L âŠ‚ T âˆ—M a Lagrangian submanifold Hamiltonianly isotopic to the zero section. We prove that if L isâ€¦ (More)

We introduce a notion of Denjoy sub-system that generalizes the one of Aubry-Mather set. For such systems, we prove a result similar to Denjoy theorem (non-existence of C Denjoy sub-systems), andâ€¦ (More)