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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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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DOI: https://doi.org/10.1007/s00209-010-0671-z