The LMS JCM, (11) 367-380. Published 26 Nov 2008. First received 20 Mar 2008.


Rational 6-cycles under iteration of quadratic polynomials

Michael Stoll



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 x2 + c. This extends earlier results by Morton for N = 4 and by Flynn, Poonen and Schaefer for N = 5.

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Appendix A : This appendix contains a MAGMA script for performing the computations reported in the paper.

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