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math.DS2025
Parabolic Implosion in the Parameter Space of Cubic Polynomials
Runze Zhang
Parabolic implosion describes the enrichment of Julia sets when a parabolic fixed point is perturbed. It is also natural to study parabolic implosion in parameter spaces. In partic…
math.DS2024
Rigidity of bounded type cubic Siegel polynomials
Jonguk Yang, Runze Zhang
We prove that if two non-renormalizable cubic Siegel polynomials with bounded type rotation numbers are combinatorially equivalent, then they are also conformally equivalent. As a…