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Constructor University（Constructor大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过有理映射的退化方法，证明次数为$d$的有理映射中任意$2d-2$个不同周期轨道的乘子代数独立，条件为至多$d$个不动点，并改进了早期结果。
AI 中文摘要
利用有理映射的退化与周期乘子的局部渐近行为，我们证明：对每个$d\ge 2$，任意$2d-2$个不同的次数为$d$的有理映射周期轨道，其乘子在$\mathbb C$上代数独立，前提是所选轨道中至多有$d$个为不动点。该条件是最优的，因为全纯指标公式关联了$d+1$个不动点的乘子。本文结果去除了早期工作中对周期的额外限制。证明通过对次数进行归纳，归纳步骤使用单孔退化，而在例外次数为四的情形使用三孔退化。
英文摘要
Using degenerations of rational maps and local asymptotics of periodic multipliers, we prove that for every $d\ge 2$, the multipliers of any $2d-2$ distinct periodic orbits of degree $d$ rational maps are algebraically independent over $\mathbb C$, provided that at most $d$ of the selected orbits are fixed points. This condition is sharp because of the Holomorphic Index Formula that relates the multipliers of the $d+1$ fixed points. The result of this paper removes the additional restrictions on periods present in earlier work. The proof proceeds by induction on the degree, using a one-hole degeneration for the induction step and a three-hole degeneration in an exceptional degree four case.
