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

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arxiv 1707.09779 v2 pith:MOXRERCZ submitted 2017-07-31 math.DS

Nataliya Goncharuk , Yulij Ilyashenko , Nikita Solodovnikov This is my paper · ORCID
classification math.DS
keywords familiesgenericbifurcationscycleglobalone-parameterparabolicabove
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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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  1. New structurally unstable families of planar vector fields

    math.DS 2019-08 conditional novelty 6.0 of 10

    Transverse 3-parameter unfoldings of vector fields with 'ears' or 'glasses' separatrix graphs carry the numerical invariant φ = -ln ρ / ln λ, so every such family is structurally unstable.

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