Expanding Thurston maps as quotients

Meyer, Daniel
(2009) Expanding Thurston maps as quotients.

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A Thurston map is a branched covering map $f\colon S^2\to S^2$ that is postcritically finite. Mating of polynomials, introduced by Douady and Hubbard, is a method to geometrically combine the Julia sets of two polynomials (and their dynamics) to form a rational map. We show that for every expanding Thurston map $f$ every sufficiently high iterate $F=f^n$ is obtained as the mating of two polynomials. One obtains a concise description of $F$ via critical portraits. The proof is based on the construction of the invariant Peano curve from Meyer. As another consequence we obtain a large number of fractal tilings of the plane and the hyperbolic plane.

Item Type: Article
Additional Information: 58 pages, 11 figures
Uncontrolled Keywords: math.CV, math.CV, math.DS, math.MG, 37F20, 37F10
Depositing User: Symplectic Admin
Date Deposited: 29 Aug 2018 09:10
Last Modified: 19 Jan 2023 01:26
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3025601