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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2506.09948 |
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- We show that for a general rational function $A$ of degree $m \geq 2$, any decomposition of its iterate $A^{\circ n}$, $n \geq 1$, into a composition of indecomposable rational functions is equivalent to the decomposition $A^{\circ n}$ itself. As an application, we prove that if $(A_1, A_2)$ is a pair of general rational functions, then the endomorphism of $\mathbb C\mathbb P^1 \times \mathbb C\mathbb P^1$ given by $ (z_1, z_2) \mapsto (A_1(z_1), A_2(z_2)) $ admits a periodic curve that is neither a vertical nor a horizontal line if and only if $A_1$ and $A_2$ are conjugate.