Chaotic Dynamics In A Family Of Set-Valued Functions
Isaac Woods
Christopher Newport University
James Kelly
Christopher Newport University
Abstract
We explore the topological dynamics of a family of set-valued functions introduced by W. T. Ingram in 2015. We focus on three particular properties associated with chaotic behavior: Devaney chaos, the specification property, and positive topological entropy. We show that for certain parameters, the function exhibits all three forms of chaos. We also discuss interesting patterns that arise in the periodic points.
