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The research group has lately begun an investigation on its implications on the dynamics of quasi-integrable Hamiltonian systems, with a particular focus on asymptotic estimates that rely on the integrability of one-dimensional systems. We intend now to proceed this investigation, and extend it to the much wider field of systems with at least two degrees of freedom. In relation to the symplectic homogenization approach, we will reconstruct the deep relations between the two different origins of homogenization, giving much finer estimates of some asymptotic behaviors that can be found in quantum, semi-classical mechanics. For this goal we will also use the above cited theorem of symplectic rigidity. Lastly, to involve asymptotic weak KAM aspects like Davini-Siconolfi results.
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