4 critical points have been found for a differential equation over a sphere ($R^2$ together with the point at infinity) represented by a vector field $F$. One is a stable focus node and the others are saddle points. Is it possible that there be no other critical points?
I'm completely lost with this. My attempt was to try and find an example hoping for a "yes" answer, but I haven't been successful. I tried to find any vector field in $R^2$ that has 3 saddle points and then add the focus point at infinity by introducing a factor to each component that spirals outwards, but this creates another unstable focus point at the origin.
Any thoughts?