In this MO post I search for some index interpretation for the number of attractors of a dynamical system.
The initial operator we associate to a vector field is the derivation operator. Theoretically, the codimension of the range of this derivation operator is an upper bound for the number of limit cycles of the vector field. But there some some practical difficulties. The main difficulty is that this codimension is almost always infinity. So in the above post I search for some remedies and resolutions for such difficulties.
I would appreciate if you give comment on the above MO question.