The turnpike property of discrete-time control problems arising in economic dynamics

In this work we study the structure of approximate solutions of a nonautonomous discrete-time control system in a compact metric space $X$ which is determined by a sequence of continuous functions $v_i: X \times X \to R^1$, $i=0,\pm 1,\pm 2,$.... The main result in this paper deals with the turnpike property of optimal control problems. To have this property means that the approximate solutions of the problems are determined mainly by the the sequence $\{v_i\}_{i=-\infty}^{\infty}$, and are essentially independent of the choice of interval and endpoint conditions, except in regions close to the endpoints.