A finiteness result for common zeros of iterates of rational maps
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866918316601245696 |
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| author | Noytaptim, Chatchai Zhong, Xiao |
| author_facet | Noytaptim, Chatchai Zhong, Xiao |
| contents | Answering a question asked by Hsia and Tucker in their paper on the finiteness of greatest common divisors of iterates of polynomials, we prove that if $f, g \in \mathbb{C}(X)$ are compositionally independent rational functions and $c \in \mathbb{C}(X)$, then there are at most finitely many $λ\in\mathbb{C}$ with the property that there is an $n$ such that $f^n(λ) = g^n(λ) = c(λ)$, except for a few families of $f, g \in Aut(\mathbb{P}^1_\mathbb{C})$ which gives counterexamples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_15104 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A finiteness result for common zeros of iterates of rational maps Noytaptim, Chatchai Zhong, Xiao Dynamical Systems Number Theory 37P05, 37P30 Answering a question asked by Hsia and Tucker in their paper on the finiteness of greatest common divisors of iterates of polynomials, we prove that if $f, g \in \mathbb{C}(X)$ are compositionally independent rational functions and $c \in \mathbb{C}(X)$, then there are at most finitely many $λ\in\mathbb{C}$ with the property that there is an $n$ such that $f^n(λ) = g^n(λ) = c(λ)$, except for a few families of $f, g \in Aut(\mathbb{P}^1_\mathbb{C})$ which gives counterexamples. |
| title | A finiteness result for common zeros of iterates of rational maps |
| topic | Dynamical Systems Number Theory 37P05, 37P30 |
| url | https://arxiv.org/abs/2405.15104 |