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arXiv:1611.09281 [math.DS]AbstractReferencesReviewsResources

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

Matthieu Arfeux, Jan Kiwi

Published 2016-11-28Version 1

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.

Comments: 17 pages, 4 figures
Categories: math.DS
Subjects: 37F10, 37F20, 37F30, 14H10
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