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THE QUADRATIC DYNATOMIC CURVES ARE SMOOTH AND IRREDUCIBLE

Abstract : We reprove here the smoothness and the irreducibility of the quadratic dynatomic curves (c; z) 2 C2 j z is n-periodic for z2 + c . The smoothness is due to Douady-Hubbard. Our proof here is based on elementary calculations on the pushforwards of speci c quadratic di erentials, following Thurston and Epstein. This approach is a computational illustration of the power of the far more general transversality theory of Epstein. The irreducibility is due to Bousch, Morton and Lau-Schleicher with di erent ap- proaches. Our proof is inspired by the proof of Lau-Schleicher. We use elementary combinatorial properties of the kneading sequences instead of internal addresses.
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https://hal.archives-ouvertes.fr/hal-00610714
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Submitted on : Saturday, July 23, 2011 - 6:23:02 PM
Last modification on : Monday, March 9, 2020 - 6:15:52 PM
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  • HAL Id : hal-00610714, version 1

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Xavier Buff, Lei Tan. THE QUADRATIC DYNATOMIC CURVES ARE SMOOTH AND IRREDUCIBLE. 2011. ⟨hal-00610714⟩

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