A Geometric Approach to the Existence of Orbits with Unbounded Energy in Generic Periodic Perturbations by a Potential of Generic Geodesic Flows of ?2}

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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]).”
Stability and instability for Gevrey quasi-convex near-integrable Hamiltonian systems (2003, result): “This situation is reminiscent of the system studied by Mather [Mat93] and its variants [BT99, DLS00 ].”
TOPOLOGICAL METHODS IN THE INSTABILITY PROBLEM OF HAMILTONIAN SYSTEMS (2005, methodology): “The main difference between the models in [ DdlLS00 ] and the models in [DdlLS03a] is that the transition chains in [DdlLS03a] incorporate, besides the regular KAM tori, secondary tori or lower dimensional tori.”
GEOMETRIC PROPERTIES OF THE SCATTERING MAP OF A NORMALLY HYPERBOLIC INVARIANT MANIFOLD (2008, methodology): “In the applications to diffusion in [ DLS00 , DLS03, DLS06a] we have, for the unperturbed system the commutation of the inner map f0 and the scattering map σ0, so”