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

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

Abstract

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.

Keywords

  • Vector Field
  • Singular Point
  • Hopf Bifurcation
  • Bifurcation Diagram
  • Algebraic Curve

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This work was supported by NSERC and FCAR.

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© 1990 Springer-Verlag

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Rousseau, C. (1990). Universal unfolding of a singularity of a symmetric vector field with 7-jet C-equivalent to y ∂/∂x+(±x3 ±x6y) ∂/∂y. In: Françoise, JP., Roussarie, R. (eds) Bifurcations of Planar Vector Fields. Lecture Notes in Mathematics, vol 1455. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0085399

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  • DOI: https://doi.org/10.1007/BFb0085399

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-53509-6

  • Online ISBN: 978-3-540-46722-9

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