Defining Chaos

Abstract

This thesis is a study of the paper “Defining Chaos” by Brian Hunt and Edward Ott [1] with added details to make arguments easier to follow. They introduced a new entropy based definition of chaos called expansion entropy. A system is defined to be chaotic when the expansion entropy is positive. Some benefits of this definition of chaos are that it is applicable to attractors, repellers, and non-periodically forced systems; autonomous and nonautonomous systems; and discrete and continuous time. We will explore the different properties of expansion entropy as well as calculate the expansion entropy of different examples. Expansion entropy is compared with topological entropy under certain conditions. Lastly, the limitations of nonentropy-based definitions of chaos are analyzed.