Understanding chaos

Abstract

Over the summer of 1989 I worked as an undergraduate research student with Dr. Hayden Porter through a COSEN grant funded by the Pew Memorial Trust on a project entitled "Understanding Chaos." I studied some of the history of research in the area of nonlinear systems, and my studies so far have concentrated mainly upon the logistic equation its behavior on both the real line and the complex plane, its properties, including scaling factors among some of the structures that arise within its domain, and how it can serve as a simplified model for studies of chaos in general. This paper represents a report on work which is still in progress as well as a review of some of the literature on nonlinear dynamics and a documentation of some of our results.