This analysis reveals the relationship between polynomial properties and their Julia sets, suggesting new insights in conformal dynamics.
In this paper, we prove that a polynomial f can be determined by the conformal conjugacy class of its restriction f|_Df(∞ ) together with the hybrid class of the restriction of f to non-trivial periodic components of the filled Julia set $K(f)$. The proof is based on quasiconformal surgery.
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Inou et al. (2025) studied this question.
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