Type of DegreeMaster's Thesis
DepartmentMathematics and Statistics
MetadataShow full item record
This thesis is a study of the paper “Deﬁning Chaos” by Brian Hunt and Edward Ott  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.
- Defining Chaos.pdf