Dynamical systems, weak KAM and sympletic geometry

Published/accepted papers

  1. Symplectic G-capacities and integrable systems (with J. Palmer and Á. Pelayo)
    Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), 18 (2018), no. 1, 65-103.
  2. Weak KAM Theory for a Weakly Coupled System of Hamilton-Jacobi Equations (with D. Gomes and D. Marcon)
    Calc. Var. Partial Differential Equations 55 (2016), no. 4, 55-79.
  3. On the density function on moduli spaces of toric 4-manifolds (with Á. Pelayo)
    Adv. Geom. 16 (2016), no. 3, 291-300.
  4. Generic hyperbolicity of Aubry sets on surfaces (with G. Contreras and L. Rifford)
    Invent. Math. 200 (2015), no. 1, 201-261.
  5. Closing Aubry sets II (with L. Rifford)
    Comm. Pure Appl. Math. 68 (2015), no. 3, 345-412.
  6. Closing Aubry sets I (with L. Rifford)
    Comm. Pure Appl. Math. 68 (2015), no. 2, 210-285.
  7. On the Hausdorff Dimension of the Mather quotient (with A. Fathi and L. Rifford)
    Comm. Pure Appl. Math. 62 (2009), no. 4, 445-500.
  8. Invariant measures of Hamiltonian systems with prescribed asymptotic Maslov index (with A. Abbondandolo)
    J. Fixed Point Theory Appl. 3 (2008), no. 1, 95-120.
  9. High action orbits for Tonelli Lagrangians and superlinear Hamiltonians on compact configuration spaces (with A. Abbondandolo)
    J. Differential Equations 234 (2007), no. 2, 626-653.

Surveys and lecture notes

  1. Aubry sets, Hamilton-Jacobi equations, and the Mañé Conjecture (with L. Rifford)
    Geometric analysis, mathematical relativity, and nonlinear partial differential equations, 83-104, Contemp. Math. 599, Amer. Math. Soc., Providence, RI, 2013.
  2. Optimal transport, Euler equations, Mather and DiPerna-Lions theories.
    Mémoire d'Habilitation à Diriger de Recherche (HDR). Nice, 2009.