Summary
We consider the question of whether multistep methods inherit in some sense quadratic first integrals possessed by the differential system being integrated. We also investigate whether, in the integration of Hamiltonian systems, multistep methods conserve the symplectic structure of the phase space.
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Eirola, T., Sanz-Serna, J.M. Conservation of integrals and symplectic structure in the integration of differential equations by multistep methods. Numer. Math. 61, 281–290 (1992). https://doi.org/10.1007/BF01385510
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DOI: https://doi.org/10.1007/BF01385510