Characteristically Near Stable Vector Fields in the Polar Complex Plane

This paper introduces results for characteristically near vector fields that are stable or non-stable in the polar complex plane $\mathbb{C}$. All characteristic vectors (aka eigenvectors) emanate from the same fixed point in $\mathbb{C}$, namely, 0. Stable characteristic vector fields satisfy an extension of the Krantz stability condition, namely, the maximal eigenvalue of a stable system lies within or on the boundary of the unit circle in $\mathbb{C}$.