A turnpike property of trajectories of dynamical systems with a lyapunov function

Abstract

In this paper, we study the structure of trajectories of discrete disperse dynamical systems with a Lyapunov function which are generated by set-valued mappings. We establish a weak version of the turnpike property which holds for all trajectories of such dynamical systems which are of a sufficient length. This result is usually true for models of economic growth which are prototypes of our dynamical systems.