Misiurewicz parameters in the exponential family

Agnieszka Badeńska

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 seriesMathematische Zeitschrift, ISSN 0025-5874, 1432-1823
Issue year2011
Vol268
No1-2
Pages291-303
Keywords in English30D05, 37F10, Entire transcendental functions, Exponential family, Julia set, Mathematics, general, Misiurewicz condition
DOIDOI:10.1007/s00209-010-0671-z
URL http://link.springer.com/article/10.1007/s00209-010-0671-z
Languageen angielski
Score (nominal)0
Citation count*4 (2016-07-16)
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