Hairs for the Complex Exponential Family

  title={Hairs for the Complex Exponential Family},
  author={Clara Bodel{\'o}n and Robert L. Devaney and Michael Hayes and Gareth O. Roberts and Lisa R. Goldberg and John H. Hubbard},
In this paper we consider both the dynamical and parameter planes for the complex exponential family Eλ(z) = λez where the parameter λ is complex. We show that there are infinitely many curves or “hairs” in the dynamical plane that contain points whose orbits underEλ tend to infinity and hence are in the Julia set. We also show that there are similar hairs in the λ-plane. In this case, the hairs contain λ-values for which the orbit of 0 tends to infinity under the corresponding exponential. In… CONTINUE READING
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