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Acta Mathematica Sinica, English Series

, Volume 33, Issue 11, pp 1536–1548 | Cite as

Analytic properties for holomorphic matrix-valued maps in ℂ2×2

  • Chao Fu
  • Ye Zhou Li
  • Xiao Yao
Article

Abstract

In this paper, we investigate some analytic properties for a class of holomorphic matrixvalued functions. In particular, we give a Picard type theorem which depicts the characterization of Picard omitting value in these functions. We also study the relation between asymptotic values and Picard omitting values, and the relation between periodic orbits of the canonical extension on ℂ2×2 and Julia set of one dimensional complex dynamic system.

Keywords

Picard theorem holomorphic matrix-value functions asymptotic values Julia set 

MR(2010) Subject Classification

30D35 

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Notes

Acknowledgements

We would like to thank Professor Zhang Guangyuan’s insights, valuable comments and encouragement during the preparation for this paper. And part of this paper has been done during Yao Xiao visits NTNU in Trondheim and Yao Xiao would like to thank Professor John Erik Fornaess’s kindness for providing such a nice opportunity.

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Copyright information

© Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.School of ScienceBeijing University of Posts and TelecommunicationsBeijingP. R. China
  2. 2.Shanghai Center Mathematical SciencesShanghaiP. R. China

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