title: Discrete dynamics versus analytic dynamics.
abstract: For discrete classical Molecular dynamics obtained by the "Verlet" algorithm (VA) with the time increment h there exists a shadow Hamiltonian H̃ with energy Ẽ(h), for which the discrete particle positions lie on the analytic trajectories for H̃. Here, we proof that there, independent of such an analytic analogy, exists an exact hidden energy invariance E(*) for VA dynamics. The fact that the discrete VA dynamics has the same invariances as Newtonian dynamics raises the question, which of the formulations that are correct, or alternatively, the most appropriate formulation of classical dynamics. In this context the relation between the discrete VA dynamics and the (general) discrete dynamics investigated by Lee [Phys. Lett. B 122, 217 (1983)] is presented and discussed.
authors: DNRF Centre "Glass and Time," IMFUFA, Department of Sciences, Roskilde University, Postbox 260, DK-4000 Roskilde, Denmark.
authors: Søren
authors: S
authors: Toxvaerd