Abstract
This chapter discusses the global asymptotic stability of optimal control systems with applications to the theory of economic growth. The qualitative study of optimal economic growth has attracted the attention of economic theorists for a few years. One major focus of this research has been to find sufficient conditions on models of economic growth for the convergence of growth paths to a steady state. In this symposium volume of the Journal of Economic Theory, Cass and Shell present the Hamiltonian formulation of competitive dynamical systems that arise in capital theory. The chapter presents a set of sufficient conditions on the Hamiltonian for such dynamical systems to converge to a steady state as time tends to infinity. The chapter also presents new results that build on the work of Cass and Shell, Rockafellar, and Hartman and Olech. It discusses the three basic types of results obtained and their relation to the literature.
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