Mathematical Theory of Economic Dynamics and Equilibria

1 Theory of point-set maps.- 1.1 Introductory concepts.- 1.2 Superlinear functionals and convex sets.- 1.3 Elements of the topological theory of point-set maps.- 1.4 Superlinear maps and their duals.- 2 The Neumann-Gale model.- 2.1 Formulation of the Neumann-Gale model.- 2.2 Rates of growth in the Neumann-Gale model.- 2.3 Spectral theory of superlinear maps.- 3 Optimal trajectories and their characteristics.- 3.1 A general technological model of economic dynamics.- 3.2 Characteristics of optimal trajectories.- 3.3 Characteristics of optimal trajectories in some concrete models.- 3.4 Generalized technological models.- 3.5 Characteristics of trajectories of infinite-dimensional models.- 4 Asymptotes of optimal trajectories.- 4.1 The weak turnpike theorem.- 4.2 Strong turnpike theorem.- 4.3 The strongest turnpike theorem.- 4.4 Asymptotes of trajectories of general technological models.- 5 Models of economic equilibria.- 5.1 n-person games.- 5.2 A finite-horizon model of economic equilibria.- 5.3 Competitive equilibria and optimality.- 6 Models of economic dynamics with explicit consumption.- 6.1 Definition of the general model of economic dynamics-its relation to the technological model.- 6.2 The turnpike.- 6.3 Economic equilibria on infinite intervals and U-optimal trajectories.- Historical comments and comments about the literature.- References.