Matilda Galmar: Dynamics of Quadratic Polynomials –a Real Approach to Chaos–

Abstract.

In this thesis we present theory regarding dynamical systems; by which we refer to the process of iterating a function. In particular, the focus is on the real-valued affine family of functions and the real-valued quadratic family of functions. We present concepts such as orbits and fixed points, as well as methods to graphically examine these for given functions. Further, we examine how the character of a fixed point affects the behavior of neighbouring points. Lastly, the Period-3 Theorem is presented and used as a stepping stone into the theory of chaos, which we conclude with a brief overview using symbolic dynamics.