On roots of unity in orbits of rational functions

Alina Ostafe

doi:10.1090/proc/13433

On roots of unity in orbits of rational functions

Alina Ostafe^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

12 Citations (Scopus)

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
Pages (from-to)	1927-1936
Number of pages	10
Journal	Proceedings of the American Mathematical Society
Volume	145
Issue number	5
DOIs	https://doi.org/10.1090/proc/13433
Publication status	Published - 2017
Externally published	Yes

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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.",

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AU - Ostafe, Alina

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N2 - 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.

AB - 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.

UR - https://www.scopus.com/pages/publications/85013661741

U2 - 10.1090/proc/13433

DO - 10.1090/proc/13433

M3 - Article

AN - SCOPUS:85013661741

SN - 0002-9939

VL - 145

SP - 1927

EP - 1936

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 5

ER -

On roots of unity in orbits of rational functions

Abstract

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