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arXiv · 1504.00985

On quadratic periodic points of quadratic polynomials

Zhiming Wang·Robin Zhang
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Abstract

Bounding the number of preperiodic points of quadratic polynomials with rational coefficients is one case of the Uniform Boundedness Conjecture in arithmetic dynamics. Here, we provide a general framework that may reduce finding periodic points of such polynomials over Galois extensions of $\mathbb{Q}$ to finding periodic points over the rationals. Furthermore, we present evidence that there are no such polynomials (up to linear conjugation) with periodic points of exact period 5 in quadratic fields by searching for points on an algebraic curve that classifies quadratic periodic points of exact period 5 and suggesting the application of the method of Chabauty and Coleman for further progress.

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Zhiming Wang, Robin Zhang. 2015-04-04. On quadratic periodic points of quadratic polynomials. https://arxiv.org/abs/1504.00985

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