Bifurcation of Homoclinic Orbits to a Saddle-Center in Reversible Systems

We consider two-parameter families of reversible vector fields having (at the critical parameter value) a homoclinic orbit to a nonhyperbolic fixed point. The nonhyperbolicity is due to a pair of purely imaginary eigenvalues. We give a complete description of the bifurcating one-homoclinic orbits to the center manifold. For that purpose we adapt Lin's method.