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

2016/11/28 by Matthieu Arfeux, Arfeux, Matthieu, Jan Kiwi +1
Mathematics · #14H10 #37F10 #37F20 #37F30 #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.1611.09281

openalex publication_date 2016/11/28 · openalex created_date 2022/08/29 · openalex updated_date 2026/07/28

Abstract

The space of monic centered cubic polynomials with marked critical points is\nisomorphic to C². For each n>0, the locus Sn formed by all polynomials with a\nspecified critical point periodic of exact period n forms an affine algebraic\nset. We prove that Sn is irreducible, thus giving an affirmative answer to a\nquestion posed by Milnor. (This manuscript has been withdrawn)\n

Citations

• A partial description of parameter space of rational maps of degree two: Part I

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