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Generic three-parameter unfolding of a completely degenerate germ of a vector field on ℝ3

2026/08/03 by Samuel Diangitukulu Ndimba, Aimable Sayinzoga, Bertuel Tangue Ndawa +2
Mathematics · #math.DS

paper · pdf

10 pages

arxiv created 2026/08/03 · arxiv updated 2026/08/04

Abstract

In this work, we analyze a completely degenerate germ of a real vector field at the origin of ℝ3. 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.