Boundary Values of the Thurston Pullback Map

2012/12/11 by Russell Lodge, Lodge, Russell · 1 citation
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1212.2672

openalex publication_date 2012/12/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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)=3z²/(2z³+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.

Citations

• The Weil-Petersson metric geometry

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• Characterizations of contracting Hurwitz bisets

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