%0 Journal Article
%T Lyapunov exponents, bifurcation currents and laminations in bifurcation loci
%A G. Bassanelli
%A F. Berteloot
%J Mathematics
%D 2008
%I arXiv
%X Bifurcation loci in the moduli space of degree $d$ rational maps are shaped by the hypersurfaces defined by the existence of a cycle of period $n$ and multiplier 0 or $e^{i\theta}$. Using potential-theoretic arguments, we establish two equidistribution properties for these hypersurfaces with respect to the bifurcation current. To this purpose we first establish approximation formulas for the Lyapunov function. In degree $d=2$, this allows us to build holomorphic motions and show that the bifurcation locus has a lamination structure in the regions where an attracting basin of fixed period exists.
%U http://arxiv.org/abs/0801.2590v1