Universal unfolding of a singularity of a symmetric vector field with 7-jet C-equivalent to y ∂/∂x+(±x3 ±x6y) ∂/∂y

Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1455)


In this paper we study the codimension 4 singularity at the origin for symmetric vector fields with nilpotent linear part and 7-jet C-equivalent to y ∂/∂x+(ax3+bx6y) ∂/∂y, a,b ≠ 0. For this we introduce the universal unfolding of the singularity and derive its bifurcation diagram. The methods are classical and make an extensive use of properties of elliptic integrals.


Vector Field Singular Point Hopf Bifurcation Bifurcation Diagram Algebraic Curve 
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Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  1. 1.Département de Mathématiques et de Statistique et Centre de Recherches MathématiquesUniversité de MontréalMontréal, QuébecCanada

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