We analyze three-dimensional Cr diffeomorphisms (r≥5) exhibiting a quadratic focus-saddle homoclinic tangency whose multipliers satisfy ∣λγ∣=1. For a proper three-parameter unfolding that splits the tangency, varies the argument of the stable multipliers, and controls the modulus ∣λγ∣
Nearby in the stack
, we show that a Hopf bifurcation occurs on this curve and that a homoclinic point to the bifurcating periodic orbit is present. As a consequence, the original map
f
can be
Cr
-approximated by a diffeomorphism exhibiting a coindex-one heterodimensional cycle in the saddle case.