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Geometry and ergodic theory of parabolic meromorphic functions
Xuan Zu-Xing 1,Zheng Jian-Hua 2
1. Beijing Key Laboratory of Information Service Engineering, Department of GeneralEducation, Beijing Union University, Beijing, 100101, People’s Republic of China
2.Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, People’sRepublic of China
*Correspondence author
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Funding: Beijing Natural Science Foundation(No.1132013) and The Project of Construction of Innovative Teams and Teacher Career Development for Uni（No.CIT and TCD20130513）, grantnumber 11171170 and the research fund（No.No. 20100002110012）, The first author is supported in part by NNSFC（No.No.11226089）
Opened online:27 December 2013
Accepted by: none
Citation: Xuan Zu-Xing,Zheng Jian-Hua.Geometry and ergodic theory of parabolic meromorphic functions[OL]. [27 December 2013] http://en.paper.edu.cn/en_releasepaper/content/4576334
 
 
Let $f$ be a parabolic transcendental meromorphic function with positive and finite order $ ho$ and its derivative satisfies some growth conditions. In this paper, we show the existence of conformal measures and use this basic tool to illustrate both geometrical and dynamical features of the radial Julia set. We also characterize the conformal measures supported on radial Julia sets.
Keywords:parabolic meromorphic function, Perron-Frobenius operator, pressure functions, conformal measures
 
 
 

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