Introduction to Chaotic Dynamical Systems

The emerging discipline known as chaos theory is a relatively new field of study with a diverse range of applications i.e., economics, biology, meteorology, etc.. Despite this, there is not as yet a universally accepted definition for chaos as it applies to general dynamical systems. Various approaches range from topological methods of a qualitative description to physical notions of randomness, information, and entropy in ergodic theory to the development of computational definitions and algorithms designed to obtain quantitative information. This thesis develops some of the current definitions and discusses several quantitative measures of chaos. It is intended to stimulate the interest of undergraduate and graduate students and is accessible to those with a knowledge of advanced calculus and ordinary differential equations. In covering chaos for continuous systems, it serves as a complement to the work done by Philip Beaver, which details chaotic dynamics for discrete systems.