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Conformal Geometry and Dynamics
Conformal Geometry and Dynamics
ISSN 1088-4173

 

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
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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
Email: r.lodge@jacobs-university.de

DOI: http://dx.doi.org/10.1090/S1088-4173-2013-00255-5
PII: S 1088-4173(2013)00255-5
Received by editor(s): November 30, 2012
Published electronically: June 6, 2013
Article copyright: © Copyright 2013 American Mathematical Society