Local Connectivity of Polynomial Julia sets at Bounded Type Siegel Boundaries

Jonguk Yang

Local Connectivity of Polynomial Julia sets at Bounded Type Siegel Boundaries

Dynamical Systems 2023-09-08 v4

Authors: Jonguk Yang

Abstract

Consider a polynomial $f$ of degree $d \geq 2$ that has a Siegel disk $\Delta_f$ with a rotation number of bounded type. We prove that there does not exist a hedgehog containing $\Delta_f$ . Moreover, if the Julia set $J_f$ of $f$ is connected, then it is locally connected at the Siegel boundary $\partial \Delta_f$ .

Keywords

polynomial julia set siegel disk bounded type local connectivity hedgehog

Cite

@article{arxiv.2010.14003,
  title  = {Local Connectivity of Polynomial Julia sets at Bounded Type Siegel Boundaries},
  author = {Jonguk Yang},
  journal= {arXiv preprint arXiv:2010.14003},
  year   = {2023}
}

Comments

51 pages, 4 figures

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