Bifurcation from heteroclinic orbits with semi-hyperbolic equilibria

Summary We study the problem of bifurcation from a heteroclinic orbit joining two semi-hyperbolic equilibrium points E₁ and E₂. We show that, if certain non-degeneracy assumptions are satisfied, E₁ and E₂ split into two equilibria E_ij, i,j= 1,2, and there are Melnikov-type conditions assuring the existence of a heteroclinic orbit from E_1i to E_2j, i,j=1,2 along directions that are tangent to the strongly-unstable (resp. strongly-stable) manifold of E_1j (resp. E_2j.Work performed under the auspicies of GNFM-CNR and within the activity of the group «Equazioni differenziali ordinarie e applicazioni»-MURST (Italy).