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.
Highlights
In [1,2] A
Our dynamical system is determined by a compact metric space of states and a transition operator
In [1,2,3,4,5,6,7] and in the present paper, this transition operator is set-valued. Such dynamical systems correspond to certain models of economic dynamics [1,8,9]
Summary
In [1,2] A. We establish a weak version of the turnpike property which hold for all trajectories of our dynamical system which are of a sufficient length and which are not necessarily approximate solutions of the problem above. The term was first coined by Samuelson in 1948 (see [14]), where he showed that an efficient expanding economy would spend most of the time in the vicinity of a balanced equilibrium path ( called a von Neumann path and a turnpike) This property was further investigated for optimal trajectories of models of economic dynamics. For related infinite horizon problems see [9,24,25,26,27,28,29,30,31]
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