A complete classification of 2 x 2 linear iterative systems

Abstract

The study of 2 x 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.