Misiurewicz parameters in the exponential family

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.
 Author Agnieszka Badeńska ZRRZ Agnieszka Badeńska,, - Department of Ordinary Differential Equations Journal series Mathematische Zeitschrift, ISSN 0025-5874, 1432-1823 Issue year 2011 Vol 268 No 1-2 Pages 291-303 Keywords in English 30D05, 37F10, Entire transcendental functions, Exponential family, Julia set, Mathematics, general, Misiurewicz condition DOI DOI:10.1007/s00209-010-0671-z URL http://link.springer.com/article/10.1007/s00209-010-0671-z Language en angielski Score (nominal) 0 Citation count* 4 (2016-07-16)
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