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Families of Hamiltonians sharing a common symmetry structure

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We describe a general procedure which allows to construct, given a family of Hamiltonians H([under q]̲,[under p]̲;[under λ]̲), a single new Hamiltonian H[over ̃]([under q]̲,[under p]̲) such that, on each level set of H[over ̃], the unparametrized orbit... ...