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arXiv · 1611.09281

Irreducibility of the set of cubic polynomials with one periodic critical point

Matthieu Arfeux·Jan Kiwi
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Abstract

The space of monic centered cubic polynomials with marked critical points is isomorphic to C^2. For each n>0, the locus Sn formed by all polynomials with a specified critical point periodic of exact period n forms an affine algebraic set. We prove that Sn is irreducible, thus giving an affirmative answer to a question posed by Milnor. (This manuscript has been withdrawn)

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Matthieu Arfeux, Jan Kiwi. 2016-11-28. Irreducibility of the set of cubic polynomials with one periodic critical point. https://arxiv.org/abs/1611.09281

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