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We follow up on our previous work (Le Bris, C. & Legoll, F. (2007) Derivation of symplectic numerical schemes for highly oscillatory Hamiltonian systems. C. R. Acad. Sci., 344, 277–282 and Le Bris, C. & Legoll, F. (2010) Integrators for highly oscillatory Hamiltonian systems: an homogenization approach. Discrete Continuous Dyn. Syst. Ser. B, 13, 347–373) which presented a possible approach for der...

Symplectic schemes for highly oscillatory Hamiltonian systems: the homogenization approach beyond the constant frequency case