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We study two existing extended phase space integrators for Hamiltoniansystems, the {\em midpoint projection method} and the {\em symmetric projectionmethod}, showing that the first is a pseudosymplectic and pseudosymmetricRunge--Kutta method and the second is a monoimplicit symplectic Runge--Kuttamethod.

Runge--Kutta methods determined from extended phase space methods for Hamiltonian systems