### 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 K^{c} 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 K^{c}. 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 |

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## Cite this

Ostafe, A. (2017). On roots of unity in orbits of rational functions.

*Proceedings of the American Mathematical Society*,*145*(5), 1927-1936. https://doi.org/10.1090/proc/13433