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Introduction

The quadratic map,


\begin{displaymath}
x_{n+1} = a - x_n^2 \qquad a,x_n \in \mathbb{R}\end{displaymath} (1)

is a well studied dynamical system whose behavior has been intensively studied and is in fact a prototypical system in the study of maps and chaotic systems.

This paper examines the effects of modifying this map in an attempt to control its behavior, in some sense, while still maintaining the fundamental structure of the dynamics of the original system (1).



URA Program Website 2004-12-02