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The coupling-constant metamorphosis is applied to modified extendedHamiltonians and sufficient conditions are found in order that the transformedhigh-degree first integral of the transformed Hamiltonian is determined by thesame algorithm which computes the corresponding first integral of the originalextended Hamiltonian. As examples, we consider the Post-Winternitz system andthe 2D caged anisotropic oscillator.

Extended Hamiltonians, Coupling-Constant Metamorphosis and the Post-Winternitz System