Document type
ArticleVersion
Accepted versionPublication date
Publication license
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/142999
Orbits of polynomial dynamical systems modulo primes
Journal Title
Director/Tutor
Additional contribution
Journal ISSN
Volume Title
Abstract
We present lower bounds for the orbit length of reduction modulo primes of parametric polynomial dynamical systems defined over the integers, under a suitable hypothesis on its set of preperiodic points over $ \mathbb{C}$. Applying recent results of Baker and DeMarco (2011) and of Ghioca, Krieger, Nguyen and Ye (2017), we obtain explicit families of parametric polynomials and initial points such that the reductions modulo primes have long orbits, for all but a finite number of values of the parameters. This generalizes a previous lower bound due to Chang (2015). As a by-product, we also slightly improve a result of Silverman (2008) and recover a result of Akbary and Ghioca (2009) as special extreme cases of our estimates.
Related resource
Subject
Subject (English)
Citation
Citation
CHANG, Mei-Chu, et al. Orbits of polynomial dynamical systems modulo primes. Proceedings of the American Mathematical Society. 2018. Vol. 146, num. 5, pags. 2015-2025. ISSN 0002-9939. [consulted: 8 of October of 2026]. Available at: https://hdl.handle.net/2445/142999