2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/115007We provide new existence and uniqueness results for the discrete-time Hamilton (DTH) equations of a symplectic-energy-momentum (SEM) integrator. In particular, we identify points in extended-phase space where the DTH equations of SEM integration have no solution for arbitrarily small time steps. We use the nonlinear pendulum to illustrate the main ideas.24 pages, see http://www.rose-hulman.edu/~shibberu/DTH_Dynamics/DTH_Dynamics.htmMathematical Physics65L12; 70H05text