Presentations of NET maps

@article{Floyd2017PresentationsON,
  title={Presentations of NET maps},
  author={W. Floyd and W. Parry and K. Pilgrim},
  journal={arXiv: Dynamical Systems},
  year={2017}
}
A branched covering $f: S^2 \to S^2$ is a nearly Euclidean Thurston (NET) map if each critical point is simple and its postcritical set has exactly four points. We show that up to equivalence, each NET map admits a normal form in terms of simple affine data. This data can then be used as input for algorithms developed for the computation of fundamental invariants, now systematically tabulated in a large census. 
Origami, Affine Maps, and Complex Dynamics
The Thurston Algorithm for quadratic matings

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Self-Similar Groups