Structure of approximate solutions for a class of optimal control systems

We study a turnpike property of approximate solutions of a discrete-time control system with a compact metric space of states which arises in economic dynamics. To have this property means that the approximate solutions of the optimal control problems are determined mainly by an objective function, and are essentially independent of the length of the interval, for all sufficiently large intervals. We show that the turnpike property is stable under perturbations of an objective function.