Abstract
Let $f_{\lambda}(z) = \lambda e^{z}$. In this short note, we consider those maps $f_{\lambda}$ with $\lambda$ close to $1$. We show that the probability that $f_{\lambda}$ is hyperbolic approaches $1$ as $\lambda \to 1$.
Citation
Xiumei Wang. Gaofei Zhang. "Most of the maps near the exponential are hyperbolic." Nagoya Math. J. 191 135 - 148, 2008.
Information
Published: 2008
First available in Project Euclid: 17 September 2008
zbMATH: 1149.37028
MathSciNet: MR2451223
Subjects:
Primary:
30D05
,
32H50
,
37F10
,
37F45
,
58F23
Rights: Copyright © 2008 Editorial Board, Nagoya Mathematical Journal
