On roots of unity in orbits of rational functions

Abstract

In this paper we characterise univariate rational functions over a number field \K having infinitely many points in the cyclotomic closure \K^c for which the orbit contains a root of unity. Our results are similar to previous results of Dvornicich and Zannier describing all polynomials having infinitely many preperiodic points in \K^c.Comment: The case of of rational functions h=f/g with deg f - deg g<0 has been removed due to a gap in the argument. The main result holds for the case deg f - deg g > 1 onl