English

Generalizations of Douady's magic formula

Dynamical Systems 2019-11-12 v1

Abstract

We generalize a combinatorial formula of Douady from the main cardioid to other hyperbolic components HH of the Mandelbrot set, constructing an explicit piecewise linear map which sends the set of angles of external rays landing on HH to the set of angles of external rays landing on the real axis.

Cite

@article{arxiv.1911.03796,
  title  = {Generalizations of Douady's magic formula},
  author = {Adam Epstein and Giulio Tiozzo},
  journal= {arXiv preprint arXiv:1911.03796},
  year   = {2019}
}

Comments

15 pages, 3 figures

R2 v1 2026-06-23T12:10:27.596Z