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ON THE ESCAPING SET OF MEROMORPHIC FUNCTIONS WITH DIRECT TRACTS

Part of: Series expansions Complex dynamical systems Differential equations in the complex domain Entire and meromorphic functions, and related topics

Published online by Cambridge University Press:  02 April 2015

ZUXING XUAN  and
JIANHUA ZHENG
ZUXING XUAN*
Affiliation:
Beijing Key Laboratory of Information Service Engineering, Institute of Applied Sciences, Department of General Education, Beijing Union University, Beijing 100101, PR China email xuanzuxing@ss.buaa.edu.cn, zuxingxuan@163.com
JIANHUA ZHENG
Affiliation:
Department of Mathematical Sciences, Tsinghua University, Beijing 100084, PR China email jzheng@math.tsinghua.edu.cn
*
✉zuxingxuan@163.com
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Abstract

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Let $f$ be a transcendental meromorphic function with at least one direct tract. In this note, we investigate the structure of the escaping set which is in the same direct tract. We also give a theorem about the slow escaping set.

Keywords

meromorphic functiondirect tractescaping set

MSC classification

Primary: 30B20: Random power series
Secondary: 30D05: Functional equations in the complex domain, iteration and composition of analytic functions 30D10: Representations of entire functions by series and integrals 34M05: Entire and meromorphic solutions 37F10: Polynomials; rational maps; entire and meromorphic functions
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 92 , Issue 1 , August 2015 , pp. 68 - 76
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

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