  We study stability and bifurcations in holomorphic families of polynomial
automorphisms of C^2. We say that such a family is weakly stable over some
parameter domain if periodic orbits do not bifurcate there. We first show that
this defines a meaningful notion of stability, which parallels in many ways the
classical notion of J-stability in one-dimensional dynamics. In the second part
of the paper, we prove that under an assumption of moderate dissipativity, the
parameters displaying homoclinic tangencies are dense in the bifurcation locus.
This confirms one of Palis' Conjectures in the complex setting. The proof
relies on the formalism of semi-parabolic bifurcation and the construction of
"critical points" in semi-parabolic basins (which makes use of the classical
Denjoy-Carleman-Ahlfors and Wiman Theorems).
