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math.DS2024
Thurston's pullback map, invariant covers, and the global dynamics on curves
Mario Bonk, Mikhail Hlushchanka, Russell Lodge
We consider rational maps on the Riemann sphere with an -invariant set of four marked points containing the postcrit…
math.DS2018
Puzzles and the Fatou-Shishikura injection for rational Newton maps
Kostiantyn Drach, Russell Lodge, Dierk Schleicher +1
We establish a principle that we call the Fatou-Shishikura injection for Newton maps of polynomials: there is a dynamically natural injection from the set of non-repelling periodic…
math.DS2012★ 5 cited
Boundary Values of the Thurston Pullback Map
Russell Lodge
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 p…