This talk introduces results for characteristically close [Fibonacci] vector fields [4] that are stable or non-stable in the polar complex plane $\mathbb{C}$, extending results in [3, 5]. All characteristic vectors emanate from the same fixed point in $\mathbb{C}$, namely, 0. Stable vector fields satisfy an extension of the Krantz stability condition [1], namely, the maximal eigenvalue of a stable system lies within or on the boundary of the unit circle in $\mathbb{C}$. Stein-Weiss vector field groups are inherent in vector fields symmetric about 0 [6]. Typically, vector fields are used to construct dynamical systems [7, 54]. The focus here is on dynamical systems generated by stable characteristic vector fields ($\phi(s)$) $\in \mathbb{C}$. In general, a characteristic of an object $X$ is a mapping $\phi : \mathbb{C} \rightarrow \mathbb{C}$ with values $\phi(x) \in \mathbb{C}) \in \mathbb{C}$ that provide a system profile. Characteristically near stable systems $X, Y$ satisfy the extreme closeness condition from [4], namely, $|\phi(x \in X) - \phi(y \in Y)| \in [0, 0.5]$.