IJPAM: Volume 42, No. 4 (2008)

BORDERLINE BEHAVIOR FOR
$2 \times 2$ ITERATIVE SYSTEMS

Samer S. Habre$^1$, Jean-Marie McDill$^2$
$^1$Division of Computer Science and Mathematics
Lebanese American University
P.O. Box 13-5053, Chouran Beirut, 1102-2801, LEBANON
e-mail: shabre@lau.edu.lb
$^2$Department of Mathematics
California Polytechnic State University
San Luis Obispo, CA 93407, USA
e-mail: jmcdill@calpoly.edu


Abstract.The study of $2 \times 2$ linear iterative systems leads naturally to an analysis of the eigenvalues and eigenvectors of the corresponding system matrix. The phase portraits for such systems have been previously examined and outlined; however the outline lacks the analysis of the many borderline cases in the trace-determinant plane. In this paper we fill in some of these details and look at the general solutions for the most interesting cases in terms of eigenvectors. In particular, we find generalized eigenvectors when required.

Received: August 17, 2007

AMS Subject Classification: 39B12

Key Words and Phrases: iterative systems, classification

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 42
Issue: 4