Abstract
We consider a large class of univariate rational functions over a number field K, including all polynomials over K, and give a precise description of the exceptional set of such functions h for which there are infinitely many initial points in the cyclotomic closure Kc for which the orbit under iterations of h 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 Kc. We also pose several open questions.
Original language | English |
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Pages (from-to) | 1927-1936 |
Number of pages | 10 |
Journal | Proceedings of the American Mathematical Society |
Volume | 145 |
Issue number | 5 |
DOIs | |
Publication status | Published - 2017 |
Externally published | Yes |