We will address questions in stability of fixed points, existence of limit cycles, bifurcations and chaos. Another important area of Dynamical Systems deals with situations in which time is discrete instead of continuous. Basically, discrete D.S. consist on maps that are iterated over and over again. For instance, Newton's method could be regarded as a Dynamical System with discrete time. We are interested in the long term behavior of these iterations, specially when the map is nonlinear.
Maps are very well suited to be studied with the help of computers.
Many of the exciting chaotic phenomena are easily observed in discrete Dynamical Systems. They are not only beautiful, but they also have mathematical meaning. We will study things like the space of fractals, contractions and Iterated Function Systems. We will learn how to generated fractals using the computer. Other activities We will have special days in which we will watch videos or go to the computer lab.