eJMT Abstract
Title |
A Complete Classification of 2×2 Linear Iterative Systems |
Author |
Samer HABRE and Jean-Marie MCDILL |
Volume |
2 |
Number |
1 |
The study of 2×2 linear iterative systems is incorporated in many books on ordinary differential
equations. As in the case of linear systems of differential equations, the classification of the
equilibrium solution (0; 0) leads to an analysis of the eigenvalues and eigenvectors of the system
matrix. However the authors do not know of any textbook that investigates the phase portraits for
the many borderline cases in the trace-determinant Plane. The purpose of this paper is to fill in
these details. In addition, a recent software developed by Hubert Hohn of Massachusetts College
of Art for the purpose of this investigation is used for pictorial illustrations of these portraits.