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 $\K^c$.

arXiv commentThe 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 only