A circular vector field is defined by the function
$$F(x,y)=$$
The Jacobian of this field is
$$J=
\begin{bmatrix}
\frac{\partial F_1}{\partial x} & \frac{\partial F_1}{\partial y} \\
\frac{\partial F_2}{\partial x} & \frac{\partial F_2}{\partial y} \\
\end{bmatrix}=
\begin{bmatrix}
0 & 1\\
-1 & 0\\
\end{bmatrix}$$
Where \(F_1=y\) and \(F_2=-x\)
The eigenvalues have no real parts and are \(-i\) and \(i\)
