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Conformal Geometry and Dynamics

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Boundary values of the Thurston pullback map

Author: Russell Lodge
Journal: Conform. Geom. Dyn. 17 (2013), 77-118
MSC (2010): Primary 37F20
Published electronically: June 6, 2013
MathSciNet review: 3063048
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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 $f(z)=\frac {3z^2}{2z^3+1}$ 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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Additional Information

Russell Lodge
Affiliation: Department of Mathematics, Jacobs University, Bremen, Germany
MR Author ID: 1022713

Received by editor(s): November 30, 2012
Published electronically: June 6, 2013
Article copyright: © Copyright 2013 American Mathematical Society