Rational 6-Cycles Under Iteration of Quadratic Polynomials

DOI10.1112/S1461157000000644zbMATH Open1222.11083arXiv0803.2836OpenAlexW2963359665MaRDI QIDQ3091971

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Publication date: 15 September 2011

Published in: (Search for Journal in Brave)

Abstract: We present a proof, which is conditional on the Birch and Swinnerton-Dyer Conjecture for a specific abelian variety, that there do not exist rational numbers x and c such that x has exact period N = 6 under the iteration x |-> x^2 + c. This extends earlier results by Morton for N = 4 and by Flynn, Poonen and Schaefer for N = 5.

Full work available at URL: https://arxiv.org/abs/0803.2836

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