At both points, $\cos\theta=0$ and $\sin2\phi=0$, so both components of the <vector field> vanish. Thus \b[both points are <equilibrium points> for every parameter value]. These are regular points of the <spherical coordinates> chart: the coordinate singularity at the pole plays no role in their <linearization>.

Solution

Past exam of the mathematics course of the University of Cambridge / 2003 / iii / Paper 59 / 1 / a / Solution

 Solution (source code)