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arXiv · 1908.02693

New structurally unstable families of planar vector fields

Nataliya Goncharuk·Yury G. Kudryashov·Nikita Solodovnikov
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Abstract

We study global bifurcations in generic 3-parameter families of vector fields on $S^2$. In the recent article [arXiv:1506.06797], Ilyashenko, Kudryashov, and Schurov show that 3-parameter unfoldings of vector fields with the polycycle "tears of the heart" are structurally unstable. We consider 3-parameter unfoldings of vector fields with separatrix graphs "ears" and "glasses", and prove that these families are structurally unstable as well. We also study in more details the classical bifurcation of a saddle loop, and use it as a building block in our main example.

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Nataliya Goncharuk, Yury G. Kudryashov, Nikita Solodovnikov. 2019-08-07. New structurally unstable families of planar vector fields. https://arxiv.org/abs/1908.02693

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