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For the Toda lattice and the Holt system we consider properties of canonicaltransformations of the extended phase space, which preserve integrability. Theseparated variables are invariant under change of the time. On the other hand,mapping of the time induces transformations of the action-angles variables anda shift of the generating function of the B\"{a}cklund transformation.Comment: LaTeX2e, +amssymb.cls, 8

Properties of the canonical transformations of the time for the Toda lattice and the Henon-Heiles system