Parabolic Components in Cubic Polynomial Slice Per₁(1)

2022/10/25 by Runze Zhang, Zhang, Runze
Mathematics · #Advanced Combinatorial Mathematics #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.2210.14305

openalex publication_date 2022/10/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the boundary of every parabolic component in the cubic polynomial slice Per₁(1) is a Jordan curve by adapting the technique of para-puzzles presented in \citeRoesch1. We also give a global description of the connected locus C₁: it is the union of two main parabolic components and the limbs attached on their boundaries.

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