Abstract:

Global bifurcation theory on the sphere is now in the study of its creation. The subject of the talk is: given a degenerate vector field, determine, what part of its phase portrait actually bifurcates? The talk is devoted to an answer to this question obtained in a joint work with Natalya Goncharuk. This answer is expected to be a powerful tool in the study of classification and structural stability of generic families of vector fields on the sphere with an arbitrary number of parameters.