English

Combinatorial rigidity for some infinitely renormalizable unicritical polynomials

Dynamical Systems 2022-02-09 v4

Abstract

We prove combinatorial rigidity of infinitely renormalizable unicritical polynomials, P_c :z \mapsto z^d+c, with complex c, under the a priori bounds and a certain "combinatorial condition". This implies the local connectivity of the connectedness loci (the Mandelbrot set when d = 2) at the corresponding parameters.

Keywords

Cite

@article{arxiv.0712.3490,
  title  = {Combinatorial rigidity for some infinitely renormalizable unicritical polynomials},
  author = {Davoud Cheraghi},
  journal= {arXiv preprint arXiv:0712.3490},
  year   = {2022}
}

Comments

37 Pages; 7 figures; pre-publication version

R2 v1 2026-06-21T09:56:22.431Z