The Theory of Hamiltonian Dynamical Systems, and an Application to Economics

Abstract

A Hamiltonian dynamical system (HDS) naturally arises in the standard control problem involving optimization over time. On this ground alone, a systematic study of the basic structure of the general HDS should be extremely useful for mathematical control theory. Applications of HDS theory extend beyond models involving optimization. The classic studies of such systems were motivated by problems in celestial mechanics. While much of the analysis of my lecture will be motivated by the normative (optimizing) model of macroeconomic growth, I will show in passing how HDS theory may be useful in analyzing many positive (“nonoptimizing”) models of macroeconomic growth.