The field of iterates of a rational function
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916197381963776 |
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| author | Veneziano, Francesco Vishkautsan, Solomon |
| author_facet | Veneziano, Francesco Vishkautsan, Solomon |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_04939 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The field of iterates of a rational function Veneziano, Francesco Vishkautsan, Solomon Number Theory Dynamical Systems 37P05 (Primary) 11C08, 37P15 (Secondary) 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. |
| title | The field of iterates of a rational function |
| topic | Number Theory Dynamical Systems 37P05 (Primary) 11C08, 37P15 (Secondary) |
| url | https://arxiv.org/abs/2404.04939 |