Аннотация:
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
Язык доклада: английский
Список литературы
N. Goncharuk, Y. Ilyashenko, N. Solodovnikov, Global bifurcations in generic one-parameter families with a parabolic cycle on $S^2$, arXiv: 1707.09779