UNDERSTANDING THE CENTER OF 2 × 2 LINEAR ITERATIVE SYSTEMS

摘要

The equilibrium solution (0,0) of a 2 × 2 linear iterative system is classified as a center when the system matrix has a determinant equal to 1 and a trace in the open interval (-2, 2). Despite the fact that the general solution of such systems is known, the behavior of the solutions is still ambiguous in the case of a center. The purpose of this paper is to determine the possible behaviors of the system solutions when the equilibrium solution (0,0) is a center and to find criteria to classify the behaviors. By examining a property of the system matrix, we show that there are only two possible behaviors of the solutions. The solutions either form a closed cycle (periodic orbit) or a dense orbit.