Compactification at Infinity

Abstract

The behavior at infinity of solutions of ordinary differential equations in the plane was studied by Poincaré by compactification of the Euclidean plane into the unit two-dimensional sphere S². The same idea of compactification can be applied to RFDEs. In order to illustrate this, we present here a study on equations obtained by compactification of linear delay equations $\dot x(t) = Ax(t - 1)$ in ℝ² and in ℝ (compactified to the sphere S² and the circle S¹, respectively).