Irreducibility of periodic curves in cubic polynomial moduli space

29 Dec 2020  ·  Matthieu Arfeux, Jan Kiwi ·

In the moduli space of complex cubic polynomials with a marked critical point, given any p>=1, we prove that the loci formed by polynomials with the marked critical point periodic of period p is an irreducible curve. Thus answering a question posed by Milnor in the 90's...

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Dynamical Systems 37F10 (Primary) 47F05, 14H10 (Secondary)