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math.DS2026
Critically fixed Thurston maps: classification, recognition, and twisting
Mikhail Hlushchanka, Nikolai Prochorov
An orientation-preserving branched covering map is called a critically fixed Thurston map if fixes each of its critical points. It was recently shown that…
math.DS2025
Profinite geometric iterated monodromy groups of postcritically finite polynomials in degree 3
Mikhail Hlushchanka, Olga Lukina, Dean Wardell
In this article, we study the properties of profinite geometric iterated monodromy groups associated to polynomials. Such groups can be seen as generic representations of absolute…
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…