Mathematics for Economists IV: Linear and Nonlinear Dynamics
Studies related to Nonlinear Economic Dynamics have recently become more prominent both in micro- and macroeconomics. The mini-term IV means to introduce students to the theory of Nonlinear Dynamical Systems and show how its tools and methods are used in the investigation of dynamic economic models. The goal of this mini course is to present several important notions and ideas from this theory in a setting that is as simple as possible. Specifically, we shall first recall some basic elements of the theory of Linear Difference Equations, then we turn to the theory of Nonlinear Difference Equations, namely, one- and two-dimensional maps, including such topics as stability, bifurcation theory and routes to chaos.
The only prerequisite for the course is a standard background in calculus and linear algebra.