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Considering a family of rational maps Tnλ concerning renormalization transformation, we give a perfect description of buried points and phase transition points in the Julia set J(Tnλ). Furthermore, we prove that J(Tnλ) contains an open interval where all points are buried points for some parameters n and λ, which is according to the problem that Curry and Mayer proposed.

On buried points and phase transition points in the Julia sets concerning renormalization transformation