The field of iterates of a rational function
Number Theory
2024-04-09 v1 Dynamical Systems
Abstract
We study how the field of definition of a rational function changes under iteration. We provide a complete classification of polynomials with the property that the field of definition of one of their iterates drops in degree (over a given base field). We show with families of examples that this characterization does not hold for rational functions. Finally, we also classify fractional linear transformations with this property.
Keywords
Cite
@article{arxiv.2404.04939,
title = {The field of iterates of a rational function},
author = {Francesco Veneziano and Solomon Vishkautsan},
journal= {arXiv preprint arXiv:2404.04939},
year = {2024}
}
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15 pages