On roots of unity in orbits of rational functions

Alina Ostafe*

*Corresponding author for this work

Research output: Contribution to journalArticle

7 Citations (Scopus)


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 languageEnglish
Pages (from-to)1927-1936
Number of pages10
JournalProceedings of the American Mathematical Society
Issue number5
Publication statusPublished - 2017
Externally publishedYes

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