Discrete Dynamical Systems

3 Credits · Level: Undergraduate

This course is an introduction to the mathematical theory of discrete dynamical systems, in which the state of a changing system at a given time is a fixed function of the previous state, and the long term behavior of the system is determined by iterating (i.e. self-composing) the function over and over. This theory is used to analyze ecological models, financial processes, differential equations, and more, and also illustrates how a system with seemingly simple rules can lead to surprisingly complicated behavior. In this course we'll cover the following topics in one-dimensional dynamics: fixed point analysis, bifurcation theory, the quadratic family, chaotic systems, symbolic dynamics, Sharkovsky's theorem, and an introduction to fractals and complex dynamics. The focus of the course will be on theory supplemented by computational experimentation.