Boundary Values of the Thurston Pullback Map
Russell Lodge
TL;DR
This paper introduces an algorithm to compute boundary values of the Thurston pullback map for maps with four postcritical points, demonstrating its application on a specific quadratic map and exploring its dynamics.
Contribution
It provides a novel algorithm for boundary value computation of Thurston maps with four postcritical points and applies it to a specific quadratic map to analyze its boundary dynamics.
Findings
Algorithm successfully computes boundary values for the given Thurston map.
Boundary dynamics are characterized and used to solve an analogue of Hubbard's Twisted Rabbit problem.
Application demonstrates the method's effectiveness on a specific quadratic Thurston map.
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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Taxonomy
TopicsGeometric and Algebraic Topology · Mathematical Dynamics and Fractals · Geometry and complex manifolds