Generic three-parameter unfolding of a completely degenerate germ of a vector field on $\mathbb{R}^3$

Samuel Diangitukulu Ndimba; Aimable Sayinzoga; Bertuel Tangue Ndawa; Jonathan Ibia Kobongo; Joseph Mpulu Kikwasini

Generic three-parameter unfolding of a completely degenerate germ of a vector field on $\mathbb{R}^3$

Dynamical Systems 2026-08-03 v1

Authors: Samuel Diangitukulu Ndimba , Aimable Sayinzoga , Bertuel Tangue Ndawa , Jonathan Ibia Kobongo , Joseph Mpulu Kikwasini

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Abstract

In this work, we analyze a completely degenerate germ of a real vector field at the origin of $\mathbb{R}^3$ . We construct a generic three-parameter unfolding of this germ and identify the associated local bifurcations. We prove that the phase portrait of the unfolded system contains a one-parameter family of heteroclinic orbits connecting two hyperbolic equilibrium points.

Keywords

vector field degenerate germ unfolding bifurcation heteroclinic orbits

Cite

@article{arxiv.2608.02074,
  title  = {Generic three-parameter unfolding of a completely degenerate germ of a vector field on $\mathbb{R}^3$},
  author = {Samuel Diangitukulu Ndimba and Aimable Sayinzoga and Bertuel Tangue Ndawa and Jonathan Ibia Kobongo and Joseph Mpulu Kikwasini},
  journal= {arXiv preprint arXiv:2608.02074},
  year   = {2026}
}

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10 pages