On Thurston's pullback map
Dynamical Systems
2011-05-10 v1
Abstract
Let f: P^1 \to P^1 be a rational map with finite postcritical set P_f. Thurston showed that f induces a holomorphic map \sigma_f of the Teichmueller space T modelled on P_f to itself fixing the basepoint corresponding to the identity map (P^1, P_f) \to (P^1, P_f). We give explicit examples of such maps f showing that the following cases may occur: (1) the basepoint is an attracting fixed point, the image of \sigma_f is open and dense, and the map \sigma_f is a covering map onto its image; (2) the basepoint is a superattracting fixed point, \sigma is surjective, and \sigma is a ramified Galois covering, (3) \sigma_f is constant.
Cite
@article{arxiv.1105.1763,
title = {On Thurston's pullback map},
author = {Xavier Buff and Adam Epstein and Sarah Koch and Kevin Pilgrim},
journal= {arXiv preprint arXiv:1105.1763},
year = {2011}
}
Comments
The published version contained an error in the proof of Theorem 5.1 which is corrected in this version