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Preprints, Working Papers, ... Year : 2012

The dynatomic curves for unimodel polynomials are smooth and irreducible

Abstract

We prove here the smoothness and the irreducibility of the periodic dynatomic curves $ (c,z)\in \C^2$ such that $z$ is $n$-periodic for $z^d+c$, where $d\geq2$. We use the method provided by Xavier Buff and Tan Lei in \cite{BT} where they prove the conclusion for $d=2$. The proof for smoothness is based on elementary calculations on the pushforwards of specific quadratic differentials, following Thurston and Epstein, while the proof for irreducibility is a simplified version of Lau-Schleicher's proof by using elementary arithmetic properties of kneading sequence instead of internal addresses.
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hal-00814484 , version 1 (17-04-2013)

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Yan Gao, Ya Fei Ou. The dynatomic curves for unimodel polynomials are smooth and irreducible. 2012. ⟨hal-00814484⟩
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