Dynamics of rational maps: a current on the bifurcation locus

Let f : P 1 P 1 be a family of rational maps of degree d > 1, parametrized holomorphically by in a complex manifold X. We show that there exists a canonical closed, positive (1,1)-current T on X supported exactly on the bifurcation locus B(f ) X. If X is a Stein manifold, then the stable regime X -B(f ) is also Stein. In particular, each stable component in the space Poly d (or Rat d ) of all polynomials (or rational maps) of degree d is a domain of holomorphy.