Belyakov-Devaney bifurcation conjecture for triple Copenhagen homoclinics

Let $\gamma_{1,2,3}$ denote the short triple Copenhagen homoclinic orbits and let $\mathfrak{D}$ be the critical curve in parameter space. Belyakov-Devaney conjecture. Any parameter continuation of $\gamma_{1,2,3}$ toward $\mathfrak{D}$ results in a Belyakov-Devaney bifurcation before the family terminates. The conjecture proposes a common bifurcation mechanism for these short homoclinic families, based on the observed type II behavior.