English

Similarity at Misiurewicz Maps in the Cubic Parameter Curves

Dynamical Systems 2025-10-31 v1

Abstract

We present a proof of the conjecture by Bonifant and Milnor (see arXiv:2503.08868) regarding the similarity between the connectedness locus of the curve Sp\mathcal{S}_p at Misiurewicz parameters and their corresponding filled Julia sets in a neighborhood of the corresponding free co-critical point. The proof is in parallel with the generalization of Tan Lei's proof of similarity in the Mandelbrot set developed by Kawahira.

Keywords

Cite

@article{arxiv.2510.26515,
  title  = {Similarity at Misiurewicz Maps in the Cubic Parameter Curves},
  author = {Araceli Bonifant and Brady Young},
  journal= {arXiv preprint arXiv:2510.26515},
  year   = {2025}
}

Comments

19 pages, 3 figures