AI 中文总结
本文研究闭曲面间分支覆盖映射的函数方程，将半共轭全纯映射结果推广至更广情形，并给出环面自同态商具有抛物轨道流形的另证及推广。
AI 中文摘要
我们研究函数方程 $ f \circ p = g \circ q,$ 其中 $ f,$ $g,$ $p,$ $q$ 是闭曲面之间的分支覆盖映射。特别地，我们将紧黎曼曲面之间半共轭全纯映射的结果推广到这一更广泛的设置中。作为应用，我们给出了每个环面自同态的商具有抛物轨道流形这一事实的另一种证明，并给出了该结果的一些推广。
英文摘要
We study the functional equation $ f \circ p = g \circ q,$ where $ f,$ $g,$ $p,$ $q$ are branched covering maps between closed surfaces. In particular, we extend results on semiconjugate holomorphic maps between compact Riemann surfaces to this broader setting. As an application, we present an alternative proof of the fact that every quotient of a torus endomorphism has a parabolic orbifold, along with some extensions of this result.
