Parabolic Implosion and Julia-Lavaurs Sets in the Exponential Family |
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Authors: | Mariusz Urbański Michel Zinsmeister |
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Affiliation: | (1) University of North Texas, Denton, TX, USA;(2) Université d’Orléans, Orléans Cedex, France |
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Abstract: | We deal with all the maps from the exponential family f ε(z) = (e −1 + ε)exp(z), with ε ≥ 0. Let h ε = HD(J r,ε) be the Hausdorff dimension of the radial Julia sets J r,ε. Observing the phenomenon of parabolic implosion, it is shown that the function ε ↦ h ε is not continuous from the right. The research of the first author was supported in part by the NSF Grant DMS 0100078. |
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Keywords: | 2000 Mathematics Subject Classification: 37F353 37F45 30D05 |
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