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Parabolic Implosion and Julia-Lavaurs Sets in the Exponential Family

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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.

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Authors and Affiliations

  1. University of North Texas, Denton, TX, USA

    Mariusz Urbański

  2. Université d’Orléans, Orléans Cedex, France

    Michel Zinsmeister

Authors
  1. Mariusz Urbański
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  2. Michel Zinsmeister
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Additional information

The research of the first author was supported in part by the NSF Grant DMS 0100078.

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Urbański, M., Zinsmeister, M. Parabolic Implosion and Julia-Lavaurs Sets in the Exponential Family. Mh Math 149, 129–140 (2006). https://doi.org/10.1007/s00605-006-0426-4

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  • DOI: https://doi.org/10.1007/s00605-006-0426-4

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