Boundary Values of the Thurston Pullback Map
arXiv:1212.2672
Abstract
For any Thurston map with exactly four postcritical points, we present an algorithm to compute the Weil-Petersson boundary values of the corresponding Thurston pullback map. This procedure is carried out for the Thurston map f(z)=3z^2/(2z^3+1) originally studied by Buff, et al. The dynamics of this boundary map are investigated and used to solve the analogue of Hubbard's Twisted Rabbit problem for f.
54 pages, 15 figures