Counting Hyperbolic Components

We give formulas for the numbers of type II and type IV hyperbolic components in the space of quadratic rational maps, for all fixed periods of attractive cycles

Hyperbolic Components in Exponential Parameter Space

We discuss the space of complex exponential maps \Ek\colon z\mapsto e^{z}+\kappa. We prove that every hyperbolic component $W$ has connected boundary, and there is a conformal isomorphism \Phi_W\colon W\to\half^- which extends to a homeomorphism of pairs \Phi_W\colon(\ovl W,W)\to(\ovl\half^-,\half^-). This solves a conjecture of Baker and Rippon, and of Eremenko and Lyubich, in the affirmative. We also prove a second conjecture of Eremenko and Lyubich.Comment: To appear in: Comptes Rendues Acad Sci Paris.-- Detailed description of results can be found in ArXiv math.DS/0311480.-- 6 pages, 1 figur