Definitions of Chaos

Abstract

As a relatively new field in mathematics, chaos theory and its fundamentals have not been set. Specifically, there exist many different mathematical definitions of chaos and what it means for a function to be classified as chaotic.

This paper examines eight major definitions that either have been used to classify a function as chaotic or have been considered a major charactersitic of a chaotic function, first illustrating the ideas and definitions with the Tent function. The body of the paper is spent proving implications between definitions or examining functions that are chaotic according to one definition of chaos but not according to another.