Abstract
The authors study bifurcations from a heteroclinic manifold connecting two nonhyperbolic equilibrium P0 and P1 for a n-dimensional dynamical system. They show that under some assumptions, each equilibrium Pi splits into two equilibria p˜i and Pi(α), i = 0, 1, and find the Melnikov vector conditions assuring the existence of a heteroclinic orbit from P1(α) to P0(α) along directions that are tangent to the strong unstable (resp. strong stable) manifold of P1(α) (resp.P0(α)). The exponential trichotomy and the unified and geometrical method are used to prove their results.
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