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arXiv · 2608.02074

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
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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.

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Samuel Diangitukulu Ndimba, Aimable Sayinzoga, Bertuel Tangue Ndawa, Jonathan Ibia Kobongo, Joseph Mpulu Kikwasini. 2026-08-25. Generic three-parameter unfolding of a completely degenerate germ of a vector field on $\mathbb{R}^3$. https://arxiv.org/abs/2608.02074

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