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International conference «Real and Complex Dynamical Systems», dedicated to the to the 75th anniversary of Yu. S. Il'yashenko
November 30, 2018 15:25–15:55, Moscow, Steklov Mathematical Institute (Gubkina, 8, 9th floor)
 


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

Nikita Solodovnikov

Higher School of Economics
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MP4 650.2 Mb
MP4 295.2 Mb

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Nikita Solodovnikov
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Abstract: 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

Language: English

References
  1. N. Goncharuk, Y. Ilyashenko, N. Solodovnikov, Global bifurcations in generic one-parameter families with a parabolic cycle on $S^2$, arXiv: 1707.09779


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