When do Two Rational Functions have Locally Biholomorphic Julia Sets?
Romain Dujardin (Sorbonne Université)
MSRI: Simons Auditorium, Online/Virtual
We address the following question, whose interest was recently renewed by problems arising in arithmetic dynamics and goes back to classical work of Fatou and Julia: under which conditions does there exist a local biholomorphism between the Julia sets of two given one-dimensional rational maps? In particular we find criteria ensuring that such a local isomorphism is induced by an algebraic correspondence. This is joint work with Charles Favre and Thomas Gauthier.