Connecting orbits between static classes for generic Lagrangian systems

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Transfer of energy to high frequencies in the cubic defocusing nonlinear Schrödinger equation (2010, unknown): “[1, 2, 9–12, 27, 30, 32, 33, 37–40, 42, 43, 46, 50, 51, 64, 66, 67, 78]).”
The dynamics of pseudographs in convex Hamiltonian systems (2004, methodology): “The theory is continued in section 4, where we explain Mañé’s decomposition in static classes of the Aubry set, and the construction of homoclinic orbits, due to Fathi [18], Contreras and Paternain [11], (see also [2]) which will play a central role in section 9.”
On the Homogenization of the Hamilton-Jacobi Equation (2019, methodology): “Inspired by a strategy that had already been exploited in the context of Mather’s theory (see for example [10, 25]), the authors propose to solve this problem by considering the lift of the Hamiltonian to the so-called (maximal free) abelian cover of M , i.”