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Most of the Maps near the Exponential are Hyperbolic

Published online by Cambridge University Press:  11 January 2016

Xiumei Wang  and
Gaofei Zhang
Xiumei Wang
Affiliation:
Department of Computer Science and Information Technology, JiangSu Teachers University of Technology, Changzhou, 213001, P. R. China, [email protected]
Gaofei Zhang
Affiliation:
Department of Mathematics, Nanjing University, Nanjing, 210093, P. R. China, [email protected]
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Abstract

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Let fλ(z) = λez. In this short note, we consider those maps fλ with λ close to 1. We show that the probability that fλ is hyperbolic approaches 1 as λ → 1.

Keywords

58F2337F1037F4532H5030D05
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 191 , 2008 , pp. 135 - 148
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2008

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