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Title: Orbits of polynomial dynamical systems modulo primes
Author: Chang, Mei-Chu
D'Andrea, Carlos, 1973-
Ostafe, Alina
Shparlinski, Igor E.
Sombra, Martín
Keywords: Sistemes dinàmics complexos
Complex dynamical systems
Issue Date: 1-Feb-2018
Publisher: American Mathematical Society (AMS)
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.
Note: Versió postprint del document publicat a:
It is part of: Proceedings of the American Mathematical Society, 2018, vol. 146, num. 5, p. 2015-2025
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ISSN: 0002-9939
Appears in Collections:Articles publicats en revistes (Matemàtiques i Informàtica)

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