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.
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