Contents Online
Mathematical Research Letters
Volume 8 (2001)
Number 1
Dynamics of rational maps: a current on the bifurcation locus
Pages: 57 – 66
DOI: https://dx.doi.org/10.4310/MRL.2001.v8.n1.a7
Author
Abstract
Let $f_\lambda:\P^1\to\P^1$ be a family of rational maps of degree $d >1$, parametrized holomorphically by $\lambda$ 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 $B(f)\subset X$. 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 $\mbox{Rat}_d$) of all polynomials (or rational maps) of degree $d$ is a domain of holomorphy.
Published 1 January 2001