Analytic properties for holomorphic matrix-valued maps in ℂ2×2
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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.
KeywordsPicard theorem holomorphic matrix-value functions asymptotic values Julia set
MR(2010) Subject Classification30D35
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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.
- Yang, L.: Value Distribution Theory, Springer-Verlag, New York, 2013Google Scholar