Global bifurcations in generic one-parameter families with a parabolic cycle on $S^2$

Nataliya Goncharuk; Yulij Ilyashenko; Nikita Solodovnikov

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arXiv · 1707.09779

Global bifurcations in generic one-parameter families with a parabolic cycle on $S^2$

Nataliya Goncharuk·Yulij Ilyashenko·Nikita Solodovnikov

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Abstract

We classify global bifurcations in generic one-parameter local families of \vfs on $S^2$ with a parabolic cycle. The classification is quite different from the classical results presented in monographs on the bifurcation theory. As a by product we prove that generic families described above are structurally stable.

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Nataliya Goncharuk, Yulij Ilyashenko, Nikita Solodovnikov. 2017-07-31. Global bifurcations in generic one-parameter families with a parabolic cycle on $S^2$. https://arxiv.org/abs/1707.09779

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