We study bifurcations of cubic homoclinic tangencies in two-dimensional
symplectic maps. We distinguish two types of cubic homoclinic tangencies, and
each type gives different first return maps derived to diverse conservative
cubic H\'enon maps with quite different bifurcation diagrams. In this way, we
establish the structure of bifurcations of periodic orbits in two parameter
general unfoldings generalizing to the conservative case the results previously
obtained for the dissipative case. We also consider the problem of 1:4
resonance for the conservative cubic H\'enon maps.Comment: 20 pages, 12 figure
