Bifurcations of families of vector felds on the two-dimensional sphere

There exists pair of weakly topologically equivalent vector fields on the two-sphere with a parabolic cycle such that their generic one-parameter unfoldings are not equivalent ([1]). Classification of generic one-parameter unfoldings of vector fields with parabolic cycles is given. Any pair of weakly topologically equivalent degenerate vector fields of codimension 1 without parabolic cycle can have only equivalent oneparameter families as unfoldings.
An overview of bifurcations of generic one-parameter families and proof of the result stated above is provided.
The author is supported by RFBR project 16-01-00748-a