Fatou-Julia dichotomy of matrix-valued polynomials
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polynomialsmatrix-valuedfunctionsmathbbsetsarticleconstructcorresponding
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This article gives a precise description of the Fatou sets and Julia sets of matrix-valued polynomials in $\mathcal{M}(2,\mathbb{C})$ in terms of the corresponding polynomials in $\mathbb{C}$. Further, we construct Green functions and B\"{o}ttcher-type functions for these matrix-valued polynomials.
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