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Misiurewicz parameters in the exponential family

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Abstract

A complex exponential map is said to be Misiurewicz if the forward trajectory of the asymptotic value 0 lies in the Julia set and is bounded. We prove that the set of Misiurewicz parameters in the exponential family \({\lambda\exp(z),\lambda\in\mathbb{C}{\setminus}\{0\}}\), has the Lebesgue measure zero.

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Authors and Affiliations

  1. Faculty of Mathematics and Information Science, Warsaw University of Technology, Pl. Politechniki 1, 00-661, Warsaw, Poland

    Agnieszka Badeńska

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  1. Agnieszka Badeńska
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Correspondence to Agnieszka Badeńska.

Additional information

The research of A. Badeńska was supported in part by Polish Ministry of Science and Higher Education Grant No. N N201 0222 33.

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Badeńska, A. Misiurewicz parameters in the exponential family. Math. Z. 268, 291–303 (2011). https://doi.org/10.1007/s00209-010-0671-z

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