Dynamics of rational functions over different fields

Xin Zheng

doi:10.1117/12.2628212

22 April 2022 Dynamics of rational functions over different fields

Xin Zheng

Proceedings Volume 12163, International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2021); 121633D (2022) https://doi.org/10.1117/12.2628212
Event: International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2021), 2021, Nanjing, China

Abstract

In this article, we shall prove the following two basic results of arithmetic dynamics. Let ƒ: P¹(K) → P¹(K) be a rational function of degree 𝑑 > 1. Discovered during the research, there are different results shown with the different definitions of K. If K is an algebraically closed field of characteristic 0, then #Fix(ƒⁿ) = 𝑑ⁿ + 0(1). If K is a number field, then there are only finitely many preperiodic points of ƒ.

Citation Download Citation

Xin Zheng "Dynamics of rational functions over different fields", Proc. SPIE 12163, International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2021), 121633D (22 April 2022); https://doi.org/10.1117/12.2628212

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