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A Moser theorem for multiscale mappings

In this paper, we study the persistence of invariant tori in nearly integrable multiscale twist mappings with intersection property and high degeneracy in the integrable part. Such results are also presented for the mappings with distinct number of angles and actions, which affirms the existence of lower-dimensional invariant tori in such mappings. Hence we establish a Moser's theorem in multiscales.