Sil’nikov saddle-focus homoclinic orbits in singularly perturbed systems in dimension higher than 3

Flaviano Battelli

We consider a singularly perturbed system depending on two parameters with a normally hyperbolic centre manifold. We assume that the unperturbed system has a homoclinic orbit connecting a hyperbolic fixed point on the centre manifold. We give conditions concerning the persistence of this connecting orbit and apply the result to construct a class of singularly perturbed systems in $R^{m+2}$ which possess Sil’nikov saddle-focus homoclinic orbits.

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