Open Access
March 2015 The M-set of λexp(z)/z has infinite area
Guoping Zhan, Liangwen Liao
Nagoya Math. J. 217: 133-159 (March 2015). DOI: 10.1215/00277630-2888085


It is known that the Fatou set of the map exp(z)/z defined on the punctured plane C is empty. We consider the M-set of λexp(z)/z consisting of all parameters λ for which the Fatou set of λexp(z)/z is empty. We prove that the M-set of λexp(z)/z has infinite area. In particular, the Hausdorff dimension of the M-set is 2. We also discuss the area of complement of the M-set.


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Guoping Zhan. Liangwen Liao. "The M-set of λexp(z)/z has infinite area." Nagoya Math. J. 217 133 - 159, March 2015.


Published: March 2015
First available in Project Euclid: 6 May 2015

zbMATH: 1362.37094
MathSciNet: MR3343841
Digital Object Identifier: 10.1215/00277630-2888085

Primary: 37F10 , 37F45
Secondary: 30D05 , 32H50

Rights: Copyright © 2015 Editorial Board, Nagoya Mathematical Journal

Vol.217 • March 2015
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