Dynamics of rational maps: A current on the bifurcation locus

Let f(lambda) : P-1 --> P-1 be a family of rational maps of degree d > 1, p arametrized holomorphically by lambda in a complex manifold X. We show that there exists a canonical closed, positive (1,1)-current T on X supported e xactly on the bifurcation locus B(f) subset of 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.