Hyperbolic Components in Exponential Parameter Space Composantes hyperboliques dans l’espace des applications exponentielles

نویسنده

  • Dierk Schleicher
چکیده

We discuss the space of complex exponential maps Eκ: z 7→ e z +κ. We prove that every hyperbolic component W has connected boundary, and there is a conformal isomorphism ΦW :W → H − which extends to a homeomorphism of pairs ΦW : (W,W ) → (H − ,H−). 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 cite this article: Dierk Schleicher, C. R. Acad. Sci. Paris, Ser. I 336 (2003).

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تاریخ انتشار 2004