Hyperbolic Components in Exponential Parameter Space
Abstract
Description
We discuss the space of complex exponential maps $\Ek\colon z\mapsto e^{z}+κ$. We prove that every hyperbolic component $W$ has connected boundary, and there is a conformal isomorphism $Φ_W\colon W\to\half^-$ which extends to a homeomorphism of pairs $Φ_W\colon(\ovl W,W)\to(\ovl\half^-,\half^-)$. 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.
To appear in: Comptes Rendues Acad Sci Paris.-- Detailed description of results can be found in ArXiv math.DS/0311480.-- 6 pages, 1 figure
To appear in: Comptes Rendues Acad Sci Paris.-- Detailed description of results can be found in ArXiv math.DS/0311480.-- 6 pages, 1 figure