Module Description

Chaos theory is an area of mathematics that studies dynamical systems that are highly sensitive to changes on their conditions. Chaotic systems exhibit, among others, underlying patterns, feedback loops, repetitions, and fractals.
The main aims of this module are twofold:
To illustrate (rigorously) how simple deterministic dynamical systems are capable of extremely complicated or chaotic behaviour.
To make contact with real systems by considering a number of physically motivated examples and defining some of the tools employed to study chaotic systems in practice.
In our study we will encounter concepts such as, discrete, and continuous dynamical systems, repellers and attractors, Cantor sets, symbolic dynamics, topological conjugacy for maps, fractals, iterated function systems and Julia sets. Ideas and techniques from calculus and geometry will be important tools.