The unfoldings of a germ of vector fields in the plane with a singularity of codimension 3. (English) Zbl 0591.58022

From the introduction: ”We study germs of vector fields under the same assumptions on their linear parts as in the article by R. I. Bogdanov [Sel. Math. Sov. 1, 389-421 (1981); translation from Tr. Semin. Im. I. G. Petrovskogo 2, 37-65 (1976; Zbl 0518.58030)] however, unlike the Bogdanov assumption we assume that one coefficient of a second order term is equal to zero. These conditions define a degenerate singularity of codimension 3. The paper is also an attempt to answer Marsden’s question ”how should one break the symmetry in the Taken’s bifurcation and produce an associated structurally stable unsymmetric bifurcation” [see J. E. Marsden, Bull. Am. Math. Soc. 84, 1125-1148 (1978; Zbl 0404.35010)].
Reviewer: J.Kolomý


37G99 Local and nonlocal bifurcation theory for dynamical systems
58C25 Differentiable maps on manifolds
58K99 Theory of singularities and catastrophe theory
Full Text: EuDML


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