LMS Journal of Computation and Mathematics

Research Article

Rational 6-Cycles Under Iteration of Quadratic Polynomials

Michael Stolla1

a1 Department of Mathematics, University of Bayreuth, 95440 Bayreuth, Germany, Michael.Stoll@uni-bayreuth.de

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 xs21A6 x2 + c. This extends earlier results by Morton for N = 4 and by Flynn, Poonen and Schaefer for N = 5.

(Received March 20 2008)

(Accepted November 26 2008)