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arXiv · 2404.04939

The field of iterates of a rational function

Francesco Veneziano·Solomon Vishkautsan
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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.

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Francesco Veneziano, Solomon Vishkautsan. 2024-04-07. The field of iterates of a rational function. https://arxiv.org/abs/2404.04939

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