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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…
math.DS2022★ 1 cited
A canonical decomposition of postcritically finite rational maps and their maximal expanding quotients
Dzmitry Dudko, Mikhail Hlushchanka, Dierk Schleicher
We provide a natural canonical decomposition of postcritically finite rational maps with non-empty Fatou sets based on the topological structure of their Julia sets. The building b…