Document Type


Date of Award



Barbara Jordan-Mickey Leland School of Public Affairs (SOPA)

Degree Name

Doctor of Education

First Advisor

Professor Robert Nehs


This paper focuses on the definitions for attracting (stable) fixed points and repelling (unstable) fixed points. These terms arise as descriptions for the long term behavior of iterates of certain simple functions. The dynamical systems studied in this paper involve the iterates of points near a fixed point of a function. As the iterates of these points are studied using graphical analysis, diverse behavior relative to the fixed point can be observed. Based on this behavior, the fixed point can be characterized as attracting (stable) or repelling (unstable). Although there is no standard definition for these terms, this paper studies several definitions that have appeared in the literature.