Homoclinic orbits in degenerate reversible-equivariant systems in R6R6

We study the dynamics near an equilibrium point p0p0 of a Z2xZ2Z2xZ2-reversible vector field in R6R6 with the reversing symmetry or symmetry φφ satisfying φ2=Iφ2=I and dimFix(φ)=3dimFix(φ)=3. We deal with systems such that XX presents at p0p0 a degenerate resonance of type 0:p:q0:p:q or 0-non-resonant.   We are assuming that the linearized system of XX (at p0p0) has as eigenvalues: λ1=0λ1=0  λj=±iαjλj=±iαj, j=2,3j=2,3. Our main concern is to find conditions for the existence of families of homoclinic orbits associated to periodic orbits near the equilibrium.