Two-point boundary value problems (TPBVPs) for conservative systems are studied in the context of the stationary action principle. For sufficiently short time horizons, this converts dynamical systems into optimal control problems, and for longer time horizons, into a generalization of such control problems. One obtains a fundamental solution, whereby two-point boundary value problems are solved via max-plus convolution of the fundamental solution with a cost function related to the terminal data. The classical mass-spring system and one-dimensional wave equation are briefly discussed as examples. The n-body problem under gravitation is then discussed. There, the stationary action principle formulation is converted to a differential game, where an opposing player maximizes over a parametrized set of quadratics associated to a type of semiconvex dual of the additive inverse of the gravitational potential. The fundamental solution for the n-body problem takes the form of a set in a space whose dimension is related to the number of bodies. Once one computes this set for a specific set of masses and time-duration, solutions of a large class of TPBVPs are immediately obtainable via max-plus convolution.