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.
2000 Mathematics Subject Classification: 37F353, 37F45, 30D05
Key words: Holomorphic dynamics, parabolic implosion, Julia-Lavaurs sets, Hausdorff dimension, hyperbolic dimension, exponential functions, conformal mesures
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