Analytic Properties for Holomorphic Matrix-valued Maps in C~(2×2)

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 C~(2×2) and Julia set of one dimensional complex dynamic system.